<PAGE>   1
                                                                  EXHIBIT 10.2

FIRST UNION NATIONAL BANK                                       BANKBOSTON,N.A.



                               August 11, 1998

Eclipsys Corporation
777 East Atlantic Avenue
Suite 200
Delray Beach, Florida 33483
ATTENTION: Chief Financial Officer

Ladies and Gentlemen:

        Reference is made to the First Amended and Restated Credit
Agreement, dated as of May 29, 1998, among Eclipsys Corporation, the lenders
party thereto, First Union National Bank, as Agent, and BankBoston, N.A., as
Co-Agent (the "Credit Agreement").  Capitalized terms used herein and not
defined shall have the meanings ascribed thereto in the Credit Agreement.  We
understand that Eclipsys Corporation consummated an initial public offering of
its common stock on Friday, August 7, 1998, and that such offering was
conducted by a nationally recognized underwriter.  In addition, we understand
that such offering yielded proceeds (net of the underwriter's commission and
the underwriter's expenses of the offering) of at least $58,000,000 but less
than $60,000,000. As a result, you have requested us to amend the Credit
Agreement so that the defined term "Qualified Public Offering" means such
offering.

        Based upon your request and our understanding of your above-referenced
initial public offering, the Lenders hereby agree to amend the Credit Agreement
as follows:

        (i)     The definition of "Qualified Public Offering" in Section 1.1 of
the Credit Agreement is hereby amended to read in full as follows:

                "Qualified Public Offering" shall mean the registered initial
public offering of common stock of the Borrower, consummated on August 7, 1998,
that yielded proceeds to the Borrower of at least $58,000,000 (net of
underwriter's commission and underwriter's expenses from the offering); and 

        (ii)    The definition of "Revolving Credit Maturity Date" in Section
1.1 of the Credit Agreement is hereby amended to read in full as follows:

                "Revolving Credit Maturity Date" shall mean August 7, 2001.

        As a condition to this amendment, the Borrower hereby represents and
warrants to each Lender that (i) the representations and warranties contained
in the Credit Agreement and each of the other Credit Documents are true and
correct on and as of the date hereof (except to the extent such representations
and warranties expressly relate solely to an earlier date) as though made on
and as of the date hereof and (ii) no Default or Event of Default has occurred
and is continuing.



<PAGE>   2
Eclipsys Corporation
August 11, 1998
Page 2


        All other terms and provisions of the Credit Agreement shall continue
in full force and effect and unchanged and are hereby confirmed in all
respects.  If you are in agreement with the foregoing, please indicate your
acceptance of this amendment by signing the enclosed counterpart hereof and
returning it to the Agent.  Upon your acceptance of this amendment, such
amendment will be effective with respect to the Credit Agreement and the other 
Credit Documents as of the date hereof.

        This letter shall be governed by and construed and enforced in
accordance with the laws of the State of North Carolina (without regard to the
conflicts of law provisions thereof).  This letter may be executed in any
number of counterparts and by different parties hereto on separate counterparts,
each of which when so executed and delivered shall be an original, but all of
which shall together constitute one and the same instrument.


                                        Sincerely,
                                        
                                        FIRST UNION NATIONAL BANK, as Agent, as 
                                              a Lender, as Swingline Lender and 
                                              as Issuing Lender

                                              By:  /s/ JOSEPH H. TOWELL 
                                                   ---------------------------
                                              Name: Joseph H. Towell
                                                    --------------------------

                                              Title: Sr. V.P.
                                                     -------------------------

                                        BANKBOSTON, N.A., as Co-Agent and as a
                                              Lender

                                              By: /s/ CHARLES C. WOODARD
                                                  ----------------------------

                                              Name: Charles C. Woodard
                                                    --------------------------

                                              Title: Managing Director
                                                     -------------------------




Agreed to and accepted as of 
the date first above written:

ECLIPSYS CORPORATION

By: /s/ ROBERT J. VANARIA
    ----------------------------

Name: Robert J. Vanaria
      --------------------------

Title:   SVP - CFO
       -------------------------