<PAGE>
 
                                                                   Exhibit 10.22

                                                                  CONFORMED COPY

                 SECOND AMENDMENT dated as of March 15, 1999 (this "Amendment")

                                                                    ---------
               to the Amended and Restated Credit Agreement dated as of
               September 25, 1998 (as amended, supplemented or otherwise
               modified from time to time, the "Credit Agreement"), among
                                                ----------------              
               UNISOURCE WORLDWIDE, INC., a Delaware corporation, UNISOURCE
               CAPITAL CORPORATION, a Delaware corporation, UNISOURCE CANADA,
               INC., a Canadian corporation, the LENDERS party thereto, THE
               CHASE MANHATTAN BANK, as Administrative Agent and U.S. Collateral
               Agent, THE TORONTO-DOMINION BANK, as Canadian Agent and Canadian
               Collateral Agent, and TORONTO DOMINION (TEXAS) INC., as
               Documentation Agent.


          WHEREAS, the Company has entered into the Merger Agreement as set
forth below;

          WHEREAS, the Company and the Required Lenders are party to the First
Amendment to the Credit Agreement dated as of February 3, 1999 (the "First
Amendment");

          WHEREAS, as a result of the transactions contemplated by the Merger
Agreement, the conditions to effectiveness of the First Amendment have not and
will not be met and instead the Company has requested that certain provisions of
the Credit Agreement be amended as provided for in this Amendment; and

          WHEREAS, the undersigned Lenders are willing, on the terms and subject
to the conditions set forth herein, to so amend the Credit Agreement as provided
for in this Amendment;

          NOW, THEREFORE, the parties hereto hereby agree as follows:

     1.  Defined Terms.  Capitalized terms used and not defined herein shall
         --------------                                                     
have the meanings given to them in the Credit Agreement.

     2. Amendment.
        ----------

          (a)  Section 1.01 of the Credit Agreement is hereby amended by
     inserting the following definitions in the appropriate order:

               "'Merger' means the merger of Vulcan Acquisition Corp. into the
          Company as contemplated by the Merger Agreement."

               "'Merger Agreement' means the merger agreement dated as of
          February 28, 1999 by and among the Company, UGI Corporation and Vulcan
          Acquisition Corp."

          (b) Section 2.08 of the Credit Agreement is hereby amended by:

<PAGE>
 
                                                                               2

               (i)  inserting following the amount "300,000,000" in paragraph
          (d) thereof the following parenthetical "(less the amount of any
          reductions under paragraph (b) of this Section)"; and

               (ii) by inserting the following new paragraph (e) at the end
          thereof:

                    "(e) On the date on which the Merger becomes effective, (i)
               unless previously terminated, the Commitments shall terminate,
               (ii) the Borrowers shall repay or prepay in accordance with
               section 2.10, as the case may be, all outstanding Loans, (iii)
               the Borrowers shall cash collateralize or otherwise secure all
               outstanding  Acceptances and Letters of Credit in a manner
               reasonably satisfactory to each Lender and Issuing Bank affected
               thereby and (iv) the Borrowers shall pay all other Obligations
               owing under the Loan Documents whether or not due and payable on
               such date."

          (c) Section 5.11 of the Credit Agreement is hereby amended by:

               (i) deleting the date "March 31, 1999" therein and substituting
          therefor "the earlier of (i) September 30, 1999 and (ii) the date that
          is ninety days after any date on which any party's obligation to enter
          into the Merger pursuant to the Merger Agreement terminates for any
          reason"; and

               (ii) deleting the amount "$300,000, 000" therein and substituting
          therefor "$225,000,000".

     3.  Amendment Fee.  The Company agrees to pay to each Lender that executes
         --------------                                                        
and delivers a copy of this Amendment to the Administrative Agent (or its
counsel) on or prior to March 15, 1999, an amendment fee in an amount equal to
0.15% of such Lender's Commitment (whether used or unused) as of the Amendment
Effective Date (and after giving effect to any reduction of Commitments on the
Amendment Effective Date); provided that the Company shall have no liability for
                           --------                                             
any such amendment fee if this Amendment does not become effective.  Such
amendment fee shall be payable (i) on the Amendment Effective Date, to each
Lender entitled to receive such fee as of the Amendment Effective Date and (ii)
in the case of any Lender that becomes entitled to such fee after the Amendment
Effective Date, within two Business Days after such Lender becomes entitled to
such fee.

     4.  No Other Amendments or Waivers; Confirmation.  Except as expressly
         ---------------------------------------------                     
amended hereby, the provisions of the Credit Agreement are and shall remain in
full force and effect.

     5.  Representations and Warranties.  The Company hereby represents and
         -------------------------------                                   
warrants to the Administrative Agent and the Lenders as of the date hereof:

          (a) After giving effect to the amendments provided for herein, no
     Default or Event of Default has occurred and is continuing.

          (b) All representations and warranties of the Company contained in the
     Credit Agreement (other than representations or warranties expressly made
     only on and as of the Closing Date) are true and correct in all material
     respects on and as of the date hereof with the same force and effect as if
     made on and as of the date hereof.
<PAGE>
 
                                                                               3

          (c)  This Amendment has been duly authorized, executed and delivered
     by the Company, and each of this Amendment and the Credit Agreement as
     amended by this Amendment constitutes a legal, valid and binding obligation
     of the Company, enforceable in accordance with its terms, except to the
     extent that the enforceability thereof may be limited by applicable
     bankruptcy, insolvency, reorganization, moratorium or similar laws
     generally affecting creditors' rights and by equitable principles
     (regardless of whether enforcement is sought in equity or at law).

     6.  Effectiveness.  This Amendment shall become effective as of the date
         --------------                                                      
(the "Amendment Effective Date") on which each of the following conditions is
met: (a) the receipt by the Administrative Agent of counterparts hereof, duly
executed and delivered by the Company and the Required Lenders, (b) the
reduction of the Commitments pursuant to Section 2.08(b) to an aggregate amount
no greater than $725,000,000 and (c) the receipt by the Administrative Agent,
for the account of each Lender entitled to receive an amendment fee on the
Amendment Effective Date pursuant to Section 3 above, of such amendment fee.

     7.  Expenses.  The Company agrees to reimburse the Administrative Agent for
         ---------                                                              
its reasonable out-of-pocket expenses in connection with this Amendment,
including the reasonable fees, charges and disbursements of Cravath, Swaine &
Moore, counsel for the Administrative Agent.

     8.  GOVERNING LAW; COUNTERPARTS.  (a) THIS AMENDMENT AND THE RIGHTS AND
         ----------------------------                                       
OBLIGATIONS OF THE PARTIES HERETO SHALL BE CONSTRUED IN ACCORDANCE WITH AND
GOVERNED BY THE LAWS OF THE STATE OF NEW YORK.

          (b) This Amendment may be executed by one or more of the parties to
this Amendment on any number of separate counterparts, and all of said
counterparts taken together shall be deemed to constitute one and the same
instrument.  This Amendment may be delivered by facsimile transmission of the
relevant signature pages hereof.


          IN WITNESS WHEREOF, the parties hereto have caused this Amendment to
be duly executed and delivered by their respective proper and duly authorized
officers as of the day and year first above written.


                                      UNISOURCE WORLDWIDE, INC.


                                      By:  /s/ Kathleen M. Burns
                                         -----------------------
                                         Name: Kathleen M. Burns
                                         Title: Vice President & Treasurer


                                      THE CHASE MANHATTAN BANK
<PAGE>
 
                                                                               4

                                      By:  /s/ Jonathan E. Twichell
                                         --------------------------
                                         Name: Jonathan E. Twichell
                                         Title: Vice President
        
        
                                      THE TORONTO DOMINION BANK,
        
                                      By:  /s/ Michael A. Freeman
                                         ------------------------
                                         Name: Michael A. Freeman
                                         Title: Manager
        
        
                                      BANK OF AMERICA NATIONAL TRUST AND SAVINGS
                                      ASSOCIATION,
        
                                      By:  /s/ John W. Pocalyko
                                         ----------------------
                                         Name: John W. Pocalyko
                                         Title: Managing Director
        
        
                                      MELLON BANK, N.A.,
        
                                      By:  /s/ Donald G. Cassidy, Jr.
                                         ----------------------------
                                         Name: Donald G. Cassidy, Jr.
                                         Title: First Vice President
        
                                      NATIONSBANK, N.A.,
        
                                      By:  /s/ John W. Pocalyko
                                         ----------------------
                                         Name: John W. Pocalyko
                                         Title: Managing Director
        
        
                                      DEN DANSKE BANK, AKTIESELSKAB, CAYMAN 
                                      ISLANDS BRANCH,

                                      By:  /s/ John A. O'Neill
                                         ---------------------
                                         Name: John A. O'Neill
                                         Title: Vice President
        
                                      By:  /s/ Peter L. Hargraves
                                         ------------------------
                                         Name: Peter L. Hargraves
                                         Title: Vice President
        
        
                                      THE NORTHERN TRUST COMPANY,
<PAGE>
 
                                                                               5

                                      By:  /s/ David L. Love
                                         -------------------
                                         Name: David L. Love
                                         Title: Second Vice President
        
        
                                      PNC BANK, N.A. ,
        
                                      By:  /s/ Vicky Ziff
                                         ----------------
                                         Name: Vicky Ziff
                                         Title: Vice President
        
        
                                      THE ROYAL BANK OF CANADA,
        
                                      By:  /s/ Don S. Bryson
                                         -------------------
                                         Name: Don S. Bryson
                                         Title: Senior Manager
        
        
                                      ISTITUTO BANCARIO SAN PAOLO DI TORINO
                                      ISTITUTO MOBILIARE ITALIANO, SPA,

                                      By:  /s/ Carlo Pensico
                                         -------------------
                                         Name: Carlo Pensico
                                         Title: First Vice President
        
                                      By:  /s/ Luca Sacchi
                                         -----------------
                                         Name: Luca Sacchi
                                         Title: Vice President
        
        
                                      THE SANWA BANK, LIMITED,
        
                                      By:  /s/ Joseph E. Leo
                                         -------------------
                                         Name: Joseph E. Leo
                                         Title: Vice President and Area Manager
        
        
                                      THE BANK OF NOVA SCOTIA,
        
                                      By:  /s/ J. Alan Edwards
                                         ---------------------
                                         Name: J. Alan Edwards
                                         Title: Authorized Signatory
        
        
                                      SUNTRUST BANK, ATLANTA
<PAGE>
 
                                                                               6

        
                                      By:  /s/ Freda Bethea
                                         ------------------
                                         Name: Freda Bethea
                                         Title: Operation Officer
        
                                      By:  /s/ W. David Wisdom
                                         ---------------------
                                         Name: W. David Wisdom
                                         Title: Vice President
        
        
                                      UBS  AG, NEW YORK BRANCH
        
                                      By:  /s/ Andrew N. Taylor
                                         ----------------------
                                         Name: Andrew N. Taylor
                                         Title: Associate Director
        
                                      By:  /s/ Paula Mueller
                                         -------------------
                                         Name: Paula Mueller
                                         Title: Director
        
        
                                      WELLS FARGO BANK, N.A.,
        
                                      By:  /s/ Greg Richardson
                                         ---------------------
                                         Name: Greg Richardson
                                         Title: Vice President
        
        
                                      THE BANK OF NEW YORK,
        
                                      By:  /s/ Walter C. Parelli
                                         -----------------------
                                         Name: Walter C. Parelli
                                         Title: Vice President
        
        
                                      THE BANK OF TOKYO - MITSUBISHI      
                                      TRUST COMPANY,
        
                                      By:  /s/ M. R. Marron
                                         ------------------
                                         Name: M.R. Marron
                                         Title: Vice President
        
                                      CIBC INC.,
        
                                      By:  /s/ Gerald Girardi
                                         --------------------
                                         Name: Gerald Girardi
                                         Title: Executive Director
<PAGE>
 
                                                                               7
        
                                      FLEET NATIONAL BANK,
        
                                      By:  /s/ Jeff Lynch
                                         ----------------
                                         Name: Jeff Lynch
                                         Title: Senior Vice President
        
        
                                      FUJI BANK, LIMITED, NEW YORK BRANCH,
        
                                      By:  /s/ Raymond Ventura
                                         ---------------------
                                         Name: Raymond Ventura
                                         Title: Vice President & Manager
        
        
                                      FIRST UNION NATIONAL BANK,
        
                                      By:  /s/ Thomas C. Woodward
                                         ------------------------
                                         Name: Thomas C. Woodward
                                         Title: Senior Vice President
        
        
                                      THE YASUDA TRUST AND
                                      BANKING COMPANY LIMITED,
        
                                      By:  /s/ Junichiro Kawamura
                                         ------------------------
                                         Name: Junichiro Kawamura
                                         Title: Vice President
        
        
                                      BANK OF MONTREAL,
        
                                      By:  /s/ R.J. McClorey
                                         -------------------
                                         Name: R.J. McClorey
                                         Title: Director
        
        
                                      BANQUE NATIONALE DE PARIS,
        
                                      By:  /s/ Richard L. Sted
                                         ---------------------
                                         Name: Richard L. Sted
                                         Title: Senior Vice President
        
                                      By:  /s/ Thomas George
                                         -------------------
                                         Name: Thomas George
<PAGE>
 
                                                                               8

                                         Title: Vice President
                                                Corporate Banking Division
          
        
                                      BAYERISCHE LANDESBANK GIROZENTRALE,
        
                                      By:  /s/ Peter Obermann
                                         --------------------
                                         Name: Peter Obermann
                                         Title: Senior Vice President
        
                                      By:  /s/ James H. Boyle
                                         --------------------
                                         Name: James H. Boyle
                                         Title: Second Vice President
         
        
                                      THE INDUSTRIAL BANK OF JAPAN
                                      TRUST COMPANY

                                      By:  /s/ John Dippo
                                         ----------------
                                         Name: John Dippo
                                         Title: Senior Vice President


                                      DEUTSCHE BANK AG
                                      NEW YORK BRANCH AND/OR
                                      CAYMAN ISLANDS BRANCH

                                      By:  /s/ Hans-Josef Thiele
                                         -----------------------
                                         Name: Hans-Josef Thiele
                                         Title: Director

                                      By:  /s/ Stephan A. Wiedemann
                                         --------------------------
                                         Name: Stephan A. Wiedemann
                                         Title: Director



                                      TORONTO DOMINION (TEXAS), INC.,
                                      as U.S. Lender,

                                      By:  /s/ Anne C. Favoriti
                                         ----------------------
                                         Name: Anne C. Favoriti
                                         Title: Vice President