<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM 10-K

                        FOR ANNUAL AND TRANSITION REPORTS
                    PURSUANT TO SECTIONS 13 OR 15 (d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

                /X/ ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

                   FOR THE FISCAL YEAR ENDED DECEMBER 31, 1995
                                       OR
              / / TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

                         COMMISSION FILE NUMBER 0-16358

                              ANDOVER BANCORP, INC.
             (Exact name of registrant as specified in its charter)

                DELAWARE                                       04-2952665     
    (State or other jurisdiction of                        (I.R.S. Employer  
     incorporation or organization)                        Identification No.)

      61 MAIN STREET, ANDOVER, MA                                01810   
(Address of principal executive office)                        (Zip Code)
                                                             
       REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE: (508)749-2000

                                 ---------------

           SECURITIES REGISTERED PURSUANT TO SECTION 12(b) OF THE ACT:

                                      NONE

           SECURITIES REGISTERED PURSUANT TO SECTION 12(g) OF THE ACT:

                          COMMON STOCK, $0.10 PAR VALUE
                        PREFERRED STOCK PURCHASED RIGHTS
                                (Title of class)

     Indicate by check mark whether: the registrant (1) has filed all reports
required to be filed by Section 13 or 15 (d) of the Securities Exchange Act of
1934 during preceding 12 months (or for such shorter period that the Registrant
was required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days. Yes  X  No
                                      -----  -----

     Indicate by check mark if disclosure of delinquent filers pursuant to Item
405 of Regulation S-K is not contained herein, and will not be contained, to the
best of registrant's knowledge, in definitive proxy or information statements
incorporated by reference in Part III of this Form 10-K or any amendment to this
Form 10-K. / /

     The aggregate market value of the voting stock held by non-affiliates of
the Registrant, based on the closing sale price for the Registrant's Common
Stock on February 21, 1996 as reported by NASDAQ, was $95,861,469.

     The number of shares outstanding of each of the Registrant's classes of
Common Stock, as of the latest practicable date, is:

                 Class: Common Stock, par value $0.10 per share
              Outstanding as of February 21, 1996: 4,236,971 shares

                       DOCUMENTS INCORPORATED BY REFERENCE

     Portions of the Andover Bancorp, Inc. Definitive Notice of Annual Meeting
and Proxy Statement for the 1996 Annual Meeting of Shareholders are incorporated
by reference into Part III of Form 10-K.
<PAGE>   2
                                    FORM 10-K
                              CROSS REFERENCE INDEX

                                     Part I
<TABLE>
<CAPTION>
                                                                                        Annual
                                                                                        Report
                                                                                         Page
<S>            <C>                                                                      <C>
Item 1         Business................................................................   2

Item 2         Properties..............................................................   7

Item 3         Legal Proceedings.......................................................   7

Item 4         Submission of Matters to a Vote of Security Holders.....................  None

                                     Part II

Item 5         Market for Registrant's Common Equity and Related Stockholder Matters...   8

Item 6         Selected Financial Data.................................................   9

Item 7         Management's Discussion and Analysis of Financial Condition and
               Results of Operations...................................................  10

Item 8         Financial Statements and Supplementary Data.............................  (See Item 14 below)
                                                                                                    

Item 9         Changes in and Disagreements with Accountants on Accounting and
               Financial Disclosure....................................................  Non-Applicable
                                                                                                       
</TABLE>

                                    Part III

The information called for by Part III (Items 10 through 13) is incorporated
herein by reference from Andover's Definitive Notice of Annual Meeting and Proxy
Statement for the 1996 Annual Meeting of Stockholders to be filed with the
Securities and Exchange Commission.

                                     Part IV

<TABLE>
Item 14        Exhibits, Financial Statement Schedules and Reports on Form 8-K

<S>            <C>                                                                                              <C>
(a)(1)         Financial Statements -
                    Independent Auditors' Report.............................................................      33

                    Consolidated Balance Sheets as of December 31, 1995 and 1994.............................      34

                    Consolidated Statements of Operations for each of the years ended
                    December 31, 1995, 1994 and 1993.........................................................      35

                    Consolidated Statements of Changes in Stockholders' Equity
                    for each of the years ended December 31, 1995, 1994 and 1993.............................      36

                    Consolidated Statements of Cash Flows for each of the years ended
                    December 31, 1995, 1994 and 1993.........................................................   37-38
<PAGE>   3
                    Notes to Consolidated Financial Statements..............................................    39-61

</TABLE>

(2)            All financial statement schedules are omitted because they are
               not applicable, the data is not significant, or the required
               information is shown elsewhere in this report.

(b)            Reports on Form 8-K. There were no reports filed on Form 8-K
               during the three months ended December 31, 1995.

(c)            List of Exhibits

               Exhibits to the Form 10-K have been included only with the copies
               of the Form 10-K filed with the SEC. Upon request to Shareholder
               Relations, Andover Bancorp, Inc., 61 Main Street, Andover,
               Massachusetts 01810, copies of the individual exhibits will be
               furnished upon payment of a reasonable fee.

Exhibit No.    Description of Exhibits

3.1            Restated Certificate of Incorporation of Andover (incorporated
               herein by reference to Exhibit 3.1 to Post-Effective Amendment
               No. 1 to Andover's Registration Statement on Form S-4 No.
               33-11891 filed on March 5, 1987).

3.2            By-laws of Andover, as amended July 21, 1994(incorporated herein
               by reference to Exhibit 3.2 to Andover's Form 10-K for the fiscal
               year ended December 31, 1994).

4.1            Specimen of Andover Bancorp, Inc. common stock certificate
               (incorporated herein by reference to Exhibit 4 to Andover's
               Registration Statement on Form S-4, Registration No. 33-11891,
               filed on February 11, 1987).

4.2            Shareholder Rights Agreement between Andover Bancorp, Inc. and
               The First National Bank of Boston (incorporated herein by
               reference to an Exhibit to Andover's Current Report on Form 8-K
               dated February 21, 1989).

4.3            Amendment to Shareholder Rights Agreement between Andover
               Bancorp, Inc. and The First National Bank of Boston (incorporated
               herein by reference to Exhibit 4.2 to Andover's Current Report on
               Form 8-K dated February 12, 1990).

10.1           Employment Agreement between Andover, Andover Bank and Gerald T.
               Mulligan, dated May 16, 1991 (incorporated herein by reference to
               Exhibit 10.1 to Andover's Form 10-K for the fiscal year ended
               December 31, 1991).

10.2           Special Termination Agreement between Andover, Andover Bank and
               Gerald T. Mulligan, dated May 16, 1991, as amended and restated,
               December 17, 1992 (incorporated herein by reference to Exhibit
               10.2 to Andover's Form 10-K for the fiscal year ended December
               31, 1992).

10.3           Special Termination Agreement between Andover, Andover Bank and
               Joseph F. Casey, dated December 17, 1992, as amended and
               restated, December 23, 1993 (incorporated herein by reference to
               Exhibit 10.3 to Andover's Form 10-K for the fiscal year ended
               December 31, 1993).

10.4           Special Termination Agreement between Andover, Andover Bank and
               James D. Dawson, dated December 17, 1992, as amended and
               restated, December 23, 1993 (incorporated herein by reference to
               Exhibit 10.4 to Andover's Form 10-K for the fiscal year ended
               December 31, 1993).
<PAGE>   4
10.5           Special Termination Agreement between Andover, Andover Bank and
               Michael J. Ecker, dated December 17, 1992, as amended and
               restated, December 23, 1993 (incorporated herein by reference to
               Exhibit 10.5 to Andover's Form 10-K for the fiscal year ended
               December 31, 1993).

10.6           Special Termination Agreement between Andover, Andover Bank and
               John R. Heerwagen, dated December 17, 1992, as amended and
               restated, December 23, 1993 (incorporated herein by reference to
               Exhibit 10.6 to Andover's Form 10-K for the fiscal year ended
               December 31, 1993).

10.7           Special Termination Agreement between Andover, Andover Bank and
               Octavio C. Bolivar, dated January 24, 1994 (incorporated herein
               by reference to Exhibit 10.7 to Andover's Form 10-K for the
               fiscal year ended December 31, 1994).

10.8           Andover Savings Bank Employees' Stock Ownership Plan and Trust
               Agreement and Amendment No. 1 (incorporated herein by reference
               to Exhibit 10(c) to Andover's Annual Report on Form 10-K for the
               fiscal year ended December 31, 1987).

10.9           Andover Bancorp, Inc. Stock Option Plan dated May 8, 1986, as
               amended May 22, 1986, January 29, 1987, and November 2, 1987
               (incorporated herein by reference to Exhibit 10(h) to Andover's
               Annual Report on Form 10-K for the fiscal year ended December 31,
               1987).

10.10          Special Termination Agreement between Andover Bank and Raymond P.
               Smith, dated December 12, 1995.

10.11          Andover Bancorp, Inc. 1995 Stock Incentive Plan dated February
               16, 1995.

10.12          Deferred Compensation Plan for Directors of Andover Bancorp, Inc.
               and its Subsidiaries, effective July 1, 1993, as amended and
               restated February 22, 1996.

11             The computation of per share earnings can be readily determined
               from the material contained in the Annual Report on Form 10-K for
               the fiscal year ended December 31, 1995.

12             As the Company does not have any debt securities registered under
               Section 12 of the Securities Act of 1933, no ratio of earnings to
               fixed charges appears in this Annual Report on Form 10-K.

13             Andover Bancorp, Inc. 1995 Annual Report, which, except for those
               portions expressly incorporated herein by reference, is furnished
               only for the information of the Securities and Exchange
               Commission and is not deemed to be filed.

22             The Company has two subsidiaries, Andover Bank and Andover Bank
               NH. Andover Bank is a Massachusetts savings bank in stock form
               while Andover Bank NH is a New Hampshire guaranty savings bank in
               stock form. Both subsidiaries are included in the Consolidated
               Financial Statements filed in the Annual Report on Form 10-K for
               the fiscal year ended December 31, 1995.

23.1           Consent of KPMG Peat Marwick LLP.
<PAGE>   5
                                   SIGNATURES

         Pursuant to the requirements of Section 13 of the Securities Exchange
Act of 1934, the Company has duly caused this report to be signed on its behalf
by the undersigned, thereunto duly authorized.

                                      ANDOVER BANCORP, INC.



March 20, 1996                        By:/s/ Gerald T. Mulligan
                                         -----------------------------
                                         Gerald T. Mulligan, President
                                         and Chief Executive Officer

         Pursuant to the requirements of the Securities Exchange Act of 1934,
this Report has been signed below by the following persons on behalf of the
Company and in the capacities and on the dates indicated.

<TABLE>
<CAPTION>
Signature                                   Title                                       Date
---------                                   -----                                       ----
<S>                                         <C>                                         <C>
/s/ Gerald T. Mulligan                      President, Chief                            March 20, 1996
-------------------------------
Gerald T. Mulligan                          Executive Officer and
                                            Director (Principal
                                            Executive Officer)

/s/ Joseph F. Casey                         Chief Financial Officer                     March 20, 1996
-------------------------------             and Treasurer (Principal
Joseph F. Casey                             Financial and Accounting
                                            Officer)
                                            
/s/ Thomas F. Caffrey                       Director                                    March 20, 1996
-------------------------------
Thomas F. Caffrey

/s/ Naomi A. Gardner                        Director                                    March 20, 1996
-------------------------------
Naomi A. Gardner

/s/ Cornelius J. McCarthy                   Director                                    March 20, 1996
-------------------------------
Cornelius J. McCarthy

/s/ Clifford E. Elias                       Director                                    March 20, 1996
-------------------------------
Clifford E. Elias

/s/ Fred P. Shaheen                         Director                                    March 20, 1996
-------------------------------
Fred P. Shaheen
</TABLE>
<PAGE>   6
                              EXHIBITS TO FORM 10-K
                              Andover Bancorp, Inc.

<TABLE>
                                                   EXHIBIT INDEX
<CAPTION>
Exhibit No.                Description of Exhibit                                                Page No.
-----------                ----------------------                                                --------
<S>                        <C>                                                                 <C>
3.1                        Restated Certificate of Incorporation
                           of Andover (incorporated herein by
                           reference to Exhibit 3.1 to Post-
                           Effective Amendment No. 1 to Andover's
                           Registration Statement on Form S-4,
                           Registration No. 33-11891 filed on
                           March 5, 1987).                                                          --

3.2                        By-laws of Andover, as amended July 21,
                           1994 (incorporated herein by reference
                           to Exhibit 3.2 to Andover's Form 10-K
                           for the fiscal year ended December 31,
                           1994).                                                                   --

4.1                        Specimen of Andover Bancorp, Inc.
                           common stock certificate (incorporated
                           herein by reference to Exhibit 4 to
                           Andover's Registration Statement on
                           Form S-4, Registration No. 33-11891,
                           filed on February 11, 1987).                                             --

4.2                        Shareholder Rights Agreement between
                           Andover Bancorp, Inc. and The First
                           National Bank of Boston (incorporated herein by
                           reference to an Exhibit to Andover's Current Report
                           on Form 8-K dated February 21, 1989).                                    --

4.3                        Amendment to Shareholder Rights
                           Agreement between Andover Bancorp, Inc.
                           and The First National Bank of Boston
                           (incorporated herein by reference to
                           Exhibit 4.2 to Andover's Current Report
                           on Form 8-K dated February 12, 1990).                                    --

10.1                       Employment Agreement between Andover,
                           Andover Bank and Gerald T. Mulligan,
                           dated May 16, 1991 (incorporated herein
                           by reference to Exhibit 10.1 to
                           Andover's Form 10-K for the fiscal
                           year ended December 31, 1991).                                           --
</TABLE>
<PAGE>   7
<TABLE>
<S>                        <C>                                                                  <C>
10.2                       Special Termination Agreement between
                           Andover, Andover Bank and Gerald T.
                           Mulligan, dated May 16, 1991, as amended
                           and restated, December 17, 1992
                           (incorporated herein by reference to
                           Exhibit 10.2 to Andover's Form 10-K
                           for the fiscal year ended December 31,
                           1992).                                                                   --

10.3                       Special Termination Agreement between
                           Andover, Andover Bank and Joseph F. Casey,
                           dated December 17, 1992, as amended and
                           restated, December 23, 1993 (incorporated
                           herein by reference to Exhibit 10.3 to
                           Andover's Form 10-K for the fiscal year
                           ended December 31, 1993).                                                --

10.4                       Special Termination Agreement between
                           Andover, Andover Bank and James D. Dawson,
                           dated December 17, 1992, as amended and
                           restated, December 23, 1993 (incorporated
                           herein by reference to Exhibit 10.4 to
                           Andover's Form 10-K for the fiscal year
                           ended December 31, 1993).                                                --

10.5                       Special Termination Agreement between
                           Andover, Andover Bank and Michael J.
                           Ecker, dated December 17, 1992, as
                           amended and restated, December 23, 1993
                           (incorporated herein by reference to
                           Exhibit 10.5 to Andover's Form 10-K for
                           the fiscal year ended December 31, 1993).                                --

10.6                       Special Termination Agreement between
                           Andover, Andover Bank and John R.
                           Heerwagen, dated December 17, 1992, as
                           amended and restated, December 23, 1993
                           (incorporated herein by reference to
                           Exhibit 10.6 to Andover's Form 10-K for
                           the fiscal year ended December 31, 1993).                                --

10.7                       Special Termination Agreement between
                           Andover, Andover Bank and Octavio C.
                           Bolivar, dated January 24, 1994
                           (incorporated herein by reference to
                           Exhibit 10.7 to Andover's Form 10-K
                           for the fiscal year ended December 31,
                           1994).                                                                   --
</TABLE>
<PAGE>   8
<TABLE>
<S>                        <C>                                                                    <C>
10.8                       Andover Savings Bank Employees' Stock
                           Ownership Plan and Trust Agreement and
                           Amendment No. 1 (incorporated herein by
                           reference to Exhibit 10(c) to Andover's
                           Annual Report on Form 10-K for the
                           fiscal year ended December 31, 1987).                                     --

10.9                       Andover Bancorp, Inc. Stock Option Plan
                           dated May 8, 1986, as amended May 22,
                           1986, January 29, 1987 and November 2,
                           1987 (incorporated herein by reference
                           to Exhibit 10(h) to Andover's Annual
                           Report on Form 10-K for the fiscal year
                           ended December 31, 1987).                                                 --

10.10                      Special Termination Agreement between
                           Andover Bank and Raymond P. Smith, dated
                           December 12, 1995.                                                         9

10.11                      Andover Bancorp, Inc. 1995 Stock
                           Incentive Plan dated February 16, 1995.                                   14

10.12                      Deferred Compensation Plan for Directors
                           of Andover Bancorp, Inc. and its
                           Subsidiaries, effective July 1, 1993, as
                           amended and restated February 22, 1996.                                   22

11                         The computation of per share earnings
                           can be readily determined from the
                           material contained in the Annual Report
                           on Form 10-K for the fiscal year ended
                           December 31, 1995.                                                        --

12                         As the Company does not have any debt
                           securities registered under Section 12
                           of the Securities Act of 1933, no ratio
                           of earnings to fixed charges appears in
                           the Annual Report on Form 10-K.                                           --

13                         Andover Bancorp, Inc. 1995 Annual Report
                           which, except for those portions
                           expressly incorporated herein by
                           reference, is furnished only for the
                           information of the Securities and Exchange
                           Commission and is not deemed to be filed.                                 28

22                         The Company has two subsidiaries, Andover
                           Bank and Andover Bank NH.  Andover Bank is
                           a Massachusetts savings bank in stock form
                           while Andover Bank NH is a New Hampshire
                           guaranty savings bank in stock form.  Both
                           subsidiaries are included in the
                           Consolidated Financial Statements filed in
                           the Annual Report on Form 10-K for the
                           fiscal year ended December 31, 1995.                                      --

23.1                       Consent of KPMG Peat Marwick LLP.                                        100
</TABLE>