<PAGE>   1
                                                                   EXHIBIT 4.13

                               TRUST AGREEMENT OF

                                 USB CAPITAL VII

         This TRUST AGREEMENT of USB CAPITAL VII (the "Trust"), dated as of May
8, 2001, among (i) U.S. Bancorp, a Delaware corporation (the "Depositor"), (ii)
Wilmington Trust Company, a Delaware banking corporation, not in its individual
capacity but solely as trustee of the Trust, and (iii) David M. Moffett, Daryl
N. Bible and Lee R. Mitau, each an individual employed by the Depositor, not in
their individual capacities but solely as administrative trustees of the Trust
(each of such trustees in (ii) and (iii), a "Trustee" and collectively, the
"Trustees"). The Depositor and the Trustees hereby agrees as follows:

         1. The Trust created hereby shall be known as "USB Capital VII", in
which name the Trustees, or the Depositor to the extent provided herein, may
conduct the business of the Trust, make and execute contracts, and sue and be
sued.

         2. The Depositor hereby assigns, transfers, conveys and sets over to
the Trustees, the sum of $10. The Trustees hereby acknowledge receipt of such
amount in trust from the Depositor, which amount shall constitute the initial
trust estate. The Trustees hereby declare that they will hold the trust estate
in trust for the Depositor. It is the intention of the parties hereto that the
Trust created hereby constitute a business trust under Chapter 38 of Title 12 of
the Delaware Code, 12 Del. C. Section 3801 et seq. (the "Business Trust Act"),
and that this document constitute the governing instrument of the Trust. The
Trustees hereby are authorized and directed to execute and file a certificate of
trust with the Secretary of the State of Delaware in accordance with the
provisions of the Business Trust Act.

         3. The Depositor and the Trustees will enter into an Amended and
Restated Trust Agreement, satisfactory to each such party and substantially in
the form to be included as an exhibit to the 1933 Act Registration Statement
referred to below, to provide for the contemplated operation of the Trust
created hereby and the issuance of the Capital Securities and the Common
Securities referred to therein. Prior to the execution and delivery of such
Amended and Restated Trust Agreement, the Trustees shall not have any duty or
obligation hereunder or with respect to the trust estate, except as other wise
required by applicable law or as may be necessary to obtain prior to such
execution and delivery any licenses, consents or approvals required by
applicable law or otherwise.

         4. The Trustees hereby authorize and direct the Depositor (i) to file
with the Securities and Exchange Commission (the "Commission") and execute, in
each case on behalf of the Trust, (a) a Registration Statement on Form S-3 (the
"1933 Act Registration Statement"), including any pre-effective or
post-effective amendments to the 1933 Act Registration Statement, relating to
the registration under the Securities Act of 1933, as amended, of the Capital
Securities of the Trust and certain other securities and (b) a Registration
Statement on Form 8-A (the "1934


<PAGE>   2

Act Registration Statement") (including all pre-effective and post-effective
amendments thereto) relating to the registration of the Capital Securities of
the Trust under Section 12(b) of the Securities Exchange Act of 1934, as
amended; (ii) to file with the New York Stock Exchange (the "Exchange") and
execute on behalf of the Trust a listing application and all other applications,
statements, certificates, agreements and other instruments as shall be necessary
or desirable to cause the Capital Securities to be listed on the Exchange and
(iii) to file and execute on behalf of the Trust such applications, reports,
surety bonds, irrevocable consents, appointments of attorney for service of
process and other papers and documents as shall be necessary or desirable to
register the Capital Securities under the securities or blue sky laws of such
jurisdictions as the Depositor, on behalf of the Trust, may deem necessary or
desirable. In the event that any filing referred to above is required by the
rules and regulations of the Commission, the Exchange or state securities or
blue sky laws to be executed on behalf of the Trust by one or more of the
Trustees, each of the Trustees, in its or his capacity as Trustee of the Trust,
is hereby authorized and, to the extent so required, directed to join in any
such filing and to execute on behalf of the Trust any and all of the foregoing,
it being understood that Wilmington Trust Company, in its capacity as Trustee of
the Trust, shall not be required to join in any such filing or execute on behalf
of the Trust any such document unless required by the rules and regulations of
the Commission, the Exchange or state securities or blue sky laws. In connection
with the filings referred to above, the Depositor and David M. Moffett, Daryl N.
Bible and Lee R. Mitau, each an administrative trustee, solely in their
capacities as Trustees of the Trust, hereby constitutes and appoints David M.
Moffett, Daryl N. Bible and Lee R. Mitau, and each of them, as its or his or her
true and lawful attorneys-in-fact and agents, with full power of substitution
and resubstitution, for the Depositor or such Trustee or in the Depositor's or
such Trustee's name, place and stead, in any and all capacities, to sign any and
all amendments (including post-effective amendments) to any such filings
(including the 1933 Act Registration Statement and the 1934 Act Registration
Statement) and to file the same, with all exhibits thereto and other documents
in connection therewith, with the Commission, the Exchange and administrators of
state securities or blue sky laws, granting unto said attorneys-in-fact and
agents full power and authority to do and perform each and every act and thing
requisite and necessary to be done in connection therewith, as fully to all
intents and purposes as the Depositor or such Trustee might or could do in
person, thereby ratifying and confirming all that said attorneys-in-fact and
agents or any of them, or their respective substitute or substitutes, shall do
or cause to be done by virtue thereof.

         5. This Trust Agreement may be executed in one or more counterparts.

         6. The number of Trustees initially shall be four (4) and thereafter
the number of the Trustees shall be such number as shall be fixed from time to
time by a written instrument signed by the Depositor which may increase or
decrease the number of Trustees; provided, however, that to the extent required
by the Business Trust Act, one Trustee shall be either a natural person who is a
resident of the State of Delaware, or, if not a natural person, an entity which
has its principal place of business in the State of Delaware and otherwise meets
the requirements of applicable Delaware law. Subject to the foregoing, the
Depositor is entitled to appoint or remove without cause any Trustee at any
time. The Trustees may resign upon thirty days' prior written notice to the
Depositor.


<PAGE>   3

         7. This Trust Agreement shall be governed by, and construed in
accordance with, the laws of the State of Delaware (without regard to conflict
of laws principles).

         IN WITNESS THEREOF, the parties hereto have caused this Trust Agreement
to be duly executed as of the day and year first above written.

                              U.S. BANCORP, as Depositor


                              By:          /s/      Laura F. Bednarski
                                 _______________________________________________
                              Name:                 Laura F. Bednarski
                              Title:                Vice President

                            WILMINGTON TRUST COMPANY,
                            not in its individual capacity but solely as Trustee


                             By:          /s/      James P. Lawler
                                ________________________________________________
                             Name:                 James P. Lawler
                             Title:                Vice President


                                          /s/      David M. Moffett
                             ___________________________________________________
                             David M. Moffett, not in his individual
                               capacity but solely as Administrative Trustee


                                          /s/      Daryl N. Bible
                             ___________________________________________________
                             Daryl N. Bible, not in his individual
                               capacity but solely as Administrative Trustee


                                          /s/      Lee R. Mitau
                             ___________________________________________________
                             Lee R. Mitau, not in his individual capacity
                               but solely as Administrative Trustee