<PAGE>   1
                                                                      Exhibit 24

                                POWER OF ATTORNEY


                  The undersigned hereby appoints Lawrence J. Toal and James E.
Kelly or either of the foregoing persons acting alone, each with the full power
of substitution, as his true and lawful attorney-in-fact and agent, for him and
in his name and place, to sign the name of the undersigned in the capacity or
capacities indicated below to the Annual Report of Dime Bancorp, Inc. on Form
10-K for the year ended December 31, 1999 and any and all amendments to such
Form 10-K and to file the same, with all exhibits thereto and other documents in
connection therewith, with all necessary or appropriate governmental or other
entities, including, but not limited to, the Securities and Exchange Commission
and the New York Stock Exchange, granting to such attorney-in-fact and agent
full power and authority to perform each act necessary to be done as fully to
all intents and purposes as he might do in person, hereby ratifying and
confirming all that such attorney-in-fact and agent may lawfully do or cause to
be done by virtue hereof.

<TABLE>
<CAPTION>
                   Signature                                      Title                              Date
                   ---------                                      -----                              ----
<S>                                                <C>                                          <C>
                                                      Chairman of the Board, Chief
                                                   Executive Officer, President, Chief
  /s/ Lawrence J. Toal                              Operating Officer and a Director
----------------------------------------------
                Lawrence J. Toal                      (Principal Executive Officer)             March 28, 2000


   /s/  Derrick D. Cephas                                      A Director                       March 28, 2000
----------------------------------------------
        Derrick D. Cephas

   /s/ Frederick C. Chen                                       A Director                       March 28, 2000
----------------------------------------------
                Frederick C. Chen

   /s/ J. Barclay Collins II                                   A Director                       March 28, 2000
----------------------------------------------
              J. Barclay Collins II

   /s/ Richard W. Dalrymple                                    A Director                       March 28, 2000
----------------------------------------------
              Richard W. Dalrymple

  /s/ James F. Fulton                                          A Director                       March 28, 2000
----------------------------------------------
                 James F. Fulton

  /s/ Fred B. Koons                                            A Director                       March 28, 2000
----------------------------------------------
                  Fred B. Koons

  /s/ Virginia M. Kopp                                         A Director                       March 28, 2000
----------------------------------------------
                Virginia M. Kopp

  /s/ James M. Large, Jr.                                      A Director                       March 28, 2000
----------------------------------------------
               James M. Large, Jr.
</TABLE>
<PAGE>   2
<TABLE>
<CAPTION>
                   Signature                                      Title                              Date
                   ---------                                      -----                              ----
<S>                                                            <C>                              <C>
  /s/ John Morning                                             A Director                       March 28, 2000
----------------------------------------------
                  John Morning

  /s/ Margaret Osmer-MsQuade                                   A Director                       March 28, 2000
----------------------------------------------
             Margaret Osmer-McQuade

  /s/ Sally Hernandez-Pinero                                   A Director                       March 28, 2000
----------------------------------------------
             Sally Hernandez-Pinero

  /s/ Dr. Paul A. Qualben                                      A Director                       March 28, 2000
----------------------------------------------
               Dr. Paul A. Qualben

  /s/ Eugene G. Schulz, Jr.                                    A Director                       March 28, 2000
----------------------------------------------
              Eugene G. Schulz, Jr.

  /s/ Howard Smith                                             A Director                       March 28, 2000
----------------------------------------------
                  Howard Smith

   /s/ Dr. Norman R. Smith                                     A Director                       March 28, 2000
----------------------------------------------
               Dr. Norman R. Smith

   /s/ Ira T. Wender                                           A Director                       March 28, 2000
----------------------------------------------
                  Ira T. Wender

                                                         Chief Financial Officer                March ___, 2000
                                                      (Principal Financial Officer)
----------------------------------------------
              Anthony R. Burriesci
                                                              Controller                       March ___, 2000
                                                     (Principal Accounting Officer)
----------------------------------------------
              John F. Kennedy

</TABLE>