<PAGE>   1
 
                            SCHEDULE 14A INFORMATION
 
          PROXY STATEMENT PURSUANT TO SECTION 14(a) OF THE SECURITIES
                  EXCHANGE ACT OF 1934 (AMENDMENT NO.       )
 
FILED BY THE REGISTRANT [X]       FILED BY A PARTY OTHER THAN THE REGISTRANT [ ]
 
--------------------------------------------------------------------------------
 
Check the appropriate box:
[ ] Preliminary Proxy Statement
[X] Definitive Proxy Statement
[ ] Definitive Additional Materials
[ ] Soliciting Material Pursuant to sec.240.14a-11(c) or sec.240.14a-12
[ ] Confidential, for Use of the Commission Only (as permitted by Rule
    14a-6(e)(2))
 
                                   EG&G, Inc.
                (Name of Registrant as Specified In Its Charter)
 
                   (Name of Person(s) Filing Proxy Statement)
 
PAYMENT OF FILING FEE (CHECK THE APPROPRIATE BOX):
[X] No fee required.
[ ] Fee computed on table below per Exchange Act Rules 14a-6(i)(4) and 0-11.
 
   1) Title of each class of securities to which transaction applies:
 
   2) Aggregate number of securities to which transaction applies:
 
   3) Per unit price or other underlying value of transaction computed pursuant
      to Exchange Act Rule 0-11 (Set forth the amount on which the filing fee 
      is calculated and state how it was determined):
 
   4) Proposed maximum aggregate value of transaction:
 
   5) Total fee paid:
 
[ ] Fee paid previously with preliminary materials.
 
[ ] Check box if any part of the fee is offset as provided by Exchange Act Rule
    0-11(a)(2) and identify the filing for which the offsetting fee was paid
    previously. Identify the previous filing by registration statement number,
    or the Form or Schedule and the date of its filing.
 
   1) Amount Previously Paid:
 
   2) Form, Schedule or Registration Statement No.:
 
   3) Filing Party:
 
   4) Date Filed:
 
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<PAGE>   2
 
                                   EG&G, INC.
 
                               45 WILLIAM STREET
                         WELLESLEY, MASSACHUSETTS 02481
 
              NOTICE OF SPECIAL MEETING OF STOCKHOLDERS TO BE HELD
 
                               SEPTEMBER 10, 1999
 
     A special meeting of stockholders of EG&G, Inc. (the "Company") will be
held at the Sheraton Needham Hotel, 100 Cabot Street, Needham, Massachusetts
02194, on Friday, September 10, 1999 at 9:00 a.m., local time, to consider and
act upon the following matters:
 
     1.  To approve an amendment to the Company's Restated Articles of
         Organization to change the name of the Company to "PerkinElmer, Inc."
 
     2.  To transact such other business as may properly come before the meeting
         or any adjournment thereof.
 
     Holders of record of the Company's Common Stock at the close of business on
August 2, 1999 will be entitled to vote at the special meeting or any
adjournment thereof.
 
                                         By Order of the Board of Directors,
 
                                         TERRANCE L. CARLSON, Clerk
 
Wellesley, Massachusetts
August 10, 1999
 
                           RETURN ENCLOSED PROXY CARD
 
     YOU ARE INVITED TO ATTEND THE SPECIAL MEETING BUT YOUR ATTENDANCE IS NOT
REQUIRED. WHETHER OR NOT YOU PLAN TO ATTEND THE MEETING, THE BOARD OF DIRECTORS
URGES YOU TO COMPLETE, DATE, SIGN AND RETURN THE ENCLOSED PROXY IN THE
ACCOMPANYING ENVELOPE. PROMPT RESPONSE WILL GREATLY FACILITATE
ARRANGEMENTS FOR THE MEETING AND YOUR COOPERATION WILL BE APPRECIATED.

<PAGE>   3
 
                                   EG&G, INC.
 
                               45 WILLIAM STREET
                         WELLESLEY, MASSACHUSETTS 02481
 
              PROXY STATEMENT FOR SPECIAL MEETING OF STOCKHOLDERS
 
                               SEPTEMBER 10, 1999
 
     This Proxy Statement is furnished in connection with the solicitation of
proxies by the Board of Directors of EG&G, Inc. (the "Company"), for use at the
Special Meeting of Stockholders to be held on September 10, 1999 and at any
adjournment of that meeting (the "Special Meeting"). All shares of Common Stock,
$1.00 par value per share, of the Company (the "Common Stock") for which proxies
are submitted will be voted in accordance with the stockholders' instructions,
and if no choice is specified, the shares will be voted in favor of the matters
set forth in the accompanying Notice of Meeting. Any proxy may be revoked by a
stockholder at any time before its exercise by delivery of written revocation to
the Clerk of the Company or by voting in person at the Special Meeting.
 
VOTING SECURITIES AND VOTES REQUIRED
 
     The Board of Directors has fixed Monday, August 2, 1999 as the record date
(the "Record Date") for determining holders of Common Stock who are entitled to
vote at the Special Meeting. At the close of business on the Record Date, there
were outstanding and entitled to vote 45,854,647 shares of Common Stock. Each
share is entitled to one vote, with no cumulative voting.
 
     The holders of a majority of the shares of Common Stock outstanding and
entitled to vote at the Special Meeting shall constitute a quorum for the
transaction of business at the Special Meeting. Shares of Common Stock held by
stockholders attending the Special Meeting and shares of Common Stock
represented at the Special Meeting by proxy (including shares that abstain or do
not vote with respect to one or more of the matters presented for stockholder
approval) will be counted for purposes of determining whether a quorum exists at
the Special Meeting.
 
     The affirmative vote of the holders of a majority of the outstanding shares
of Common Stock is required for the approval of the amendment to the Company's
Restated Articles of Organization (the "Restated Articles") to be considered at
the Special Meeting.
 
     In determining whether the proposal to approve the amendment to the
Restated Articles has received the requisite number of votes, shares that
abstain from voting, and shares held in "street name" by brokers or nominees who
indicate on their proxies that they do not have discretionary authority to vote
those shares with respect to the amendment to the Restated Articles, will be
treated as outstanding shares and, accordingly, will have the same effect as a
vote against that proposal.
 
SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS
 
     The following table identifies the only persons known to the Company to be
beneficial owners of five percent or more of the outstanding shares of Common
Stock. The information in this table and the footnotes is taken from a Schedule
13G dated February 1, 1999, filed by FMR Corp., and a Schedule 13G dated

<PAGE>   4
 
February 10, 1999, filed by The Regents of the University of California, with
the Securities and Exchange Commission.
 

<TABLE>
<CAPTION>
                                                        AMOUNT AND NATURE
                                                          OF BENEFICIAL          PERCENT
         NAME AND ADDRESS OF BENEFICIAL OWNER               OWNERSHIP            OF CLASS
         ------------------------------------           -----------------        --------
<S>                                                     <C>                      <C>
FMR Corp. ............................................      5,806,561(1)          12.99%
  82 Devonshire Street
  Boston, MA 02109
The Regents of the University of California...........      3,343,781(2)            7.3%
  1111 Broadway, 14th Floor
  Oakland, CA 94607
</TABLE>

 
---------------
 
(1) The Schedule 13G filed by FMR Corp. states that FMR Corp. (i) has sole
    dispositive power with respect to 5,806,561 shares, of which 5,235,100
    shares are held by various investment companies to which a wholly-owned
    subsidiary of FMR Corp., Fidelity Management and Research Company, acts as
    investment adviser, and 571,461 shares are held by various institutional
    accounts for which Fidelity Management Trust Company, a wholly-owned
    subsidiary of FMR Corp., serves as investment manager, and (ii) has sole
    voting power with respect to 551,161 of the shares held by such
    institutional account(s).
 
(2) The Schedule 13G filed by The Regents of the University of California states
    that it has sole voting power and sole dispositive power over 3,343,781
    shares.
 
SECURITY OWNERSHIP OF MANAGEMENT
 
     The following table shows the number of shares of Common Stock owned of
record or beneficially (including unexercised stock options exercisable within
60 days) on June 30, 1999 (or such other date as is set forth in footnotes 1 and
4 below) (i) by each of the Directors of the Company, (ii) by the Company's
chief executive officer and each of the four other most highly compensated
executive officers of the Company during fiscal 1998 (the "Named Executive
Officers") and (iii) by all of the Company's executive officers and Directors as
a group. No Director or executive officer of the Company owned any equity
securities of the Company other than Common Stock on that date.
 

<TABLE>
<CAPTION>
                                                        AMOUNT AND NATURE
                                                          OF BENEFICIAL          PERCENT
                         NAME                               OWNERSHIP            OF CLASS
                         ----                           -----------------        --------
<S>                                                     <C>                      <C>
John M. Kucharski(1)..................................        310,226(2)(3)          *
Gregory L. Summe......................................        235,483(2)             *
Angelo D. Castellana..................................        112,611(2)(3)          *
John F. Alexander, II(1)..............................        223,441(2)             *
Murray Gross(1).......................................        118,644(2)             *
Tamara Erickson.......................................          2,400                *
John B. Gray(1).......................................         25,000                *
Kent F. Hansen........................................         17,200(2)             *
John F. Keane.........................................          2,400                *
Nicholas A. Lopardo...................................          3,200                *
Greta E. Marshall.....................................         17,000(2)             *
Michael C. Ruettgers..................................          2,500                *
Gabriel Schmergel.....................................          1,500                *
John Larkin Thompson..................................         10,000                *
G. Robert Tod.........................................         23,700(3)             *
All executive officers and Directors of the Company as
  a Group, 28 in number, including those listed
  above...............................................      1,425,868(2)(3)(4)     3.1%
</TABLE>

 
---------------
 
 *  Less than 1%
 
                                        2

<PAGE>   5
 
(1) At June 30, 1999, Messrs. Kucharski, Alexander, Gross and Gray no longer
    served as Named Executive Officers or Directors of the Company. The number
    of shares shown as beneficially owned by Messrs. Kucharski, Alexander, Gross
    and Gray is shown as of February 1, 1999, the latest practicable date.
 
(2) The amounts shown as beneficially owned by Messrs./Ms. Kucharski, Summe,
    Castellana, Alexander, Gross, Gray, Hansen, Marshall and Tod, and by all
    executive officers and Directors as a group, include 210,000, 160,000,
    87,600, 110,000, 85,800, 10,000, 10,000, 10,000, 10,000 and 874,960 shares,
    respectively, which are obtainable within 60 days after June 30, 1999 upon
    exercise of, and payment for, outstanding, unexercised stock options. The
    amounts shown as beneficially owned by Messr. Castellana and by all
    executive officers and Directors as a group do not include 2,584 and 4,837
    shares, respectively, which are accrued under the EG&G Deferred Compensation
    Plan and which are payable 100% in EG&G stock at the time of retirement or
    termination of employment.
 
(3) Owners of all shares shown have sole voting and investment power except
    Messrs. Kucharski and Castellana, who share investment and/or voting power
    over 32,226 shares and 7,022 shares, respectively. The number of shares
    stated as being owned beneficially includes shares held beneficially by
    spouses, minor children and certain trusts; the inclusion of such shares in
    the Proxy Statement, however, does not constitute an admission that the
    executive officers or Directors are direct or indirect beneficial owners of
    such shares.
 
(4) The number of shares shown as beneficially owned by all executive officers
    and Directors as a group includes 831,864 shares, including 548,000 shares
    which are obtainable within 60 days after June 30, 1999 upon exercise of,
    and payment for, outstanding unexercised stock options, owned by certain
    executive officers and Directors who no longer serve as executive officers
    or Directors of the Company as of June 30, 1999.
 
                       APPROVAL OF AMENDMENT TO RESTATED
                            ARTICLES OF ORGANIZATION
 
     The Board of Directors has adopted, and has recommended that the
stockholders approval at the Special Meeting, a resolution to amend the
Company's Restated Articles to change the Company's name to "PerkinElmer, Inc."
 
     In the judgment of the Board of Directors, the change of corporate name
will enable the Company to better create brand identity of its products under
the well-established Perkin Elmer name. If the proposed name change is adopted,
the Company intends to use the name "PerkinElmer, Inc." in its communications
with stockholders and the investment community.
 
     If the amendment is adopted, stockholders will not be required to exchange
outstanding stock certificates for new certificates. If approved by the
stockholders, the amendment to the Restated Articles will become effective upon
the filing of Articles of Amendment to the Restated Articles with the Secretary
of State of the Commonwealth of Massachusetts, which filing is expected to take
place shortly after the Special Meeting. If this proposal is not approved by the
stockholders, then the Articles of Amendment will not be filed.
 
     THE BOARD OF DIRECTORS BELIEVES THAT THE APPROVAL OF THE AMENDMENT TO THE
RESTATED ARTICLES IS IN THE BEST INTEREST OF THE COMPANY AND ITS STOCKHOLDERS
AND THEREFORE RECOMMENDS A VOTE "FOR" THIS PROPOSAL.
 
                                 OTHER MATTERS
 
     Management does not know of any other matters that may come before the
Special Meeting. However, if any other matters are properly presented to the
Special Meeting, it is the intention of the persons named in the accompanying
proxy to vote, or otherwise act, in accordance with their judgment on such
matters.
 
     All expenses connected with soliciting proxies will be borne by the
Company, which expects to pay brokers, nominees, fiduciaries and other
custodians their reasonable expenses for forwarding proxy materials to
principals and obtaining their voting instructions. The Company has engaged
Kissel-Blake Inc., of New York
                                        3

<PAGE>   6
 
City, to assist in soliciting proxies from brokers, nominees, fiduciaries and
custodians and has agreed to pay Kissel-Blake Inc. $7,500 and out-of-pocket
expenses for such efforts. In addition to the use of the mails, certain
directors, officers and employees may solicit proxies in person or by use of
communications media.
 
                             STOCKHOLDER PROPOSALS
 
     In order to be considered for addition to the agenda for the 2000 Annual
Meeting of Stockholders and to be included in the Proxy Statement and form of
proxy, stockholder proposals should be addressed to the Clerk of the Company and
must be received at the Corporate Offices of EG&G no later than December 3,
1999.
 
     Stockholders who wish to make a proposal at the 2000 Annual Meeting --
other than one that will be included in the Company's proxy materials -- should
notify the Company no later than February 16, 2000. If a stockholder who wishes
to present a proposal fails to notify the Company by this date, the proxies that
management solicits for the meeting will have discretionary authority to vote on
the stockholder's proposal if it is properly brought before the meeting. If a
stockholder makes a timely notification, the proxies may still exercise
discretionary voting authority under circumstances consistent with the proxy
rules of the Securities and Exchange Commission.
 
                                            By Order of the Board of Directors
 
                                            TERRANCE L. CARLSON, Clerk
 
August 10, 1999
 
     YOU ARE INVITED TO ATTEND THE SPECIAL MEETING BUT YOUR ATTENDANCE IS NOT
REQUIRED. WHETHER OR NOT YOU PLAN TO ATTEND THE MEETING, THE BOARD OF DIRECTORS
URGES YOU TO COMPLETE, DATE, SIGN AND RETURN THE ENCLOSED PROXY IN THE
ACCOMPANYING ENVELOPE. PROMPT RESPONSE WILL GREATLY FACILITATE ARRANGEMENTS FOR
THE MEETING AND YOUR COOPERATION WILL BE APPRECIATED.
 
                                        4

<PAGE>   7
 
                                                                     0886-PS3-99

<PAGE>   8


PROXY                              EG&G, INC.                              PROXY


              SPECIAL MEETING OF STOCKHOLDERS - SEPTEMBER 10, 1999

                 THIS PROXY IS SOLICITED ON BEHALF OF THE BOARD
                          OF DIRECTORS OF THE COMPANY.

     The undersigned, having received notice of the meeting and the proxy
statement therefor, and revoking all prior proxies, hereby appoint(s) Robert F.
Friel and Terrance L. Carlson, and each of them, attorneys or attorney of the
undersigned (with full power of substitution in them and each of them) for and
in the name(s) of the undersigned to attend the Special Meeting of Stockholders
of EG&G, Inc. (the "Company") to be held at the Sheraton Needham Hotel, 100
Cabot Street, Needham, Massachusetts 02194 at 9:00 a.m. (local time), on Friday,
September 10, 1999 and any adjourned sessions thereof, and there to vote and act
upon the following matter in respect of shares of Common Stock of the Company
which the undersigned would be entitled to vote or act upon, with all powers the
undersigned would possess if personally present. The following matter is being
proposed by the Company.

     IN THEIR DISCRETION, THE PROXIES ARE AUTHORIZED TO VOTE UPON SUCH OTHER
MATTERS AS MAY PROPERLY COME BEFORE THE MEETING, OR ANY ADJOURNMENT THEREOF.


                         (TO BE SIGNED ON REVERSE SIDE)




<PAGE>   9




     PLEASE MARK YOUR
     [X] VOTE AS IN THIS
     EXAMPLE.

1.   Approval of an amendment to the Company's Restated Articles of Organization
     to change the name of the Company to "PerkinElmer, Inc."

        [ ]      FOR             [ ]   AGAINST                [ ]   ABSTAIN


     THE SHARES REPRESENTED BY THIS PROXY WILL BE VOTED AS DIRECTED BY THE
UNDERSIGNED. IF NO DIRECTION IS GIVEN WITH RESPECT TO THE PROPOSAL SPECIFIED
ABOVE, THIS PROXY WILL BE VOTED FOR THE PROPOSAL.

     Attendance of the undersigned at the meeting or at any adjourned session
thereof will not be deemed to revoke this proxy unless the undersigned shall
affirmatively indicate thereat the intention of the undersigned to vote said
shares in person. If the undersigned hold(s) any of the shares of the Company in
a fiduciary, custodial or joint capacity or capacities, this proxy is signed by
the undersigned in every such capacity as well as individually.


PLEASE MARK, SIGN, DATE AND RETURN THE PROXY CARD PROMPTLY, USING THE ENCLOSED
ENVELOPE.


SIGNATURE(S) _____________________________________ DATE _______________________

NOTE:  Please sign name(s) exactly as appearing hereon.  When signing as 
       attorney, executor, administrator or other fiduciary, please give your 
       full title as such. Joint owners should each sign personally.