<PAGE>

                                                                    EXHIBIT 31.1

                                 CERTIFICATIONS

I, Hamid R. Moghadam, certify that:

     (1) I have reviewed this annual report on Form 10-K of AMB Property, L.P.;

     (2) Based on my knowledge, this report does not contain any untrue
statement of a material fact or omit to state a material fact necessary to make
the statements made, in light of the circumstances under which such statements
were made, not misleading with respect to the period covered by this report;

     (3) Based on my knowledge, the financial statements, and other financial
information included in this report, fairly present in all material respects the
financial condition, results of operations and cash flows of the registrant as
of, and for, the periods presented in this report;

     (4) The registrant's other certifying officers and I are responsible for
establishing and maintaining disclosure controls and procedures (as defined in
Exchange Act Rules 13a-15(e) and 15d-15(e)) for the registrant and have:

          a) Designed such disclosure controls and procedures, or caused such
     disclosure controls and procedures to be designed under our supervision, to
     ensure that material information relating to the registrant, including its
     consolidated subsidiaries, is made known to us by others within those
     entities, particularly during the period in which this report is being
     prepared;

          b) Evaluated the effectiveness of the registrant's disclosure controls
     and procedures and presented in this report our conclusions about the
     effectiveness of the disclosure controls and procedures, as of the end of
     the period covered by this report based on such evaluation; and

          c) Disclosed in this report any change in the registrant's internal
     control over financial reporting that occurred during the registrant's most
     recent fiscal quarter (the registrant's fourth fiscal quarter in the case
     of an annual report) that has materially affected, or is reasonably likely
     to materially affect, the registrant's internal control over financial
     reporting; and

     (5) The registrant's other certifying officers and I have disclosed, based
on our most recent evaluation of internal control over financial reporting, to
the registrant's auditors and the audit committee of the registrant's board of
directors of the registrant's general partner (or persons performing the
equivalent functions):

          a) All significant deficiencies and material weaknesses in the design
     or operation of internal control over financial reporting which are
     reasonably likely to adversely affect the registrant's ability to record,
     process, summarize and report financial information; and

          b) Any fraud, whether or not material, that involves management or
     other employees who have a significant role in the registrant's internal
     control over financial reporting.

Date: March 11, 2004

                                          By:     /s/ HAMID R. MOGHADAM
                                            ------------------------------------
                                                     Hamid R. Moghadam
                                                 Chairman of the Board and
                                                  Chief Executive Officer
                                              of AMB Property Corporation, the
                                              general partner of AMB Property,
                                                             L.P.
<PAGE>

I, W. Blake Baird, certify that:

     (1) I have reviewed this annual report on Form 10-K of AMB Property, L.P.;

     (2) Based on my knowledge, this report does not contain any untrue
statement of a material fact or omit to state a material fact necessary to make
the statements made, in light of the circumstances under which such statements
were made, not misleading with respect to the period covered by this report;

     (3) Based on my knowledge, the financial statements, and other financial
information included in this report, fairly present in all material respects the
financial condition, results of operations and cash flows of the registrant as
of, and for, the periods presented in this report;

     (4) The registrant's other certifying officers and I are responsible for
establishing and maintaining disclosure controls and procedures (as defined in
Exchange Act Rules 13a-15(e) and 15d-15(e)) for the registrant and have:

          a) Designed such disclosure controls and procedures, or caused such
     disclosure controls and procedures to be designed under our supervision, to
     ensure that material information relating to the registrant, including its
     consolidated subsidiaries, is made known to us by others within those
     entities, particularly during the period in which this report is being
     prepared;

          b) Evaluated the effectiveness of the registrant's disclosure controls
     and procedures and presented in this report our conclusions about the
     effectiveness of the disclosure controls and procedures, as of the end of
     the period covered by this report based on such evaluation; and

          c) Disclosed in this report any change in the registrant's internal
     control over financial reporting that occurred during the registrant's most
     recent fiscal quarter (the registrant's fourth fiscal quarter in the case
     of an annual report) that has materially affected, or is reasonably likely
     to materially affect, the registrant's internal control over financial
     reporting; and

     (5) The registrant's other certifying officers and I have disclosed, based
on our most recent evaluation of internal control over financial reporting, to
the registrant's auditors and the audit committee of the registrant's board of
directors of the registrant's general partner (or persons performing the
equivalent functions):

          a) All significant deficiencies and material weaknesses in the design
     or operation of internal control over financial reporting which are
     reasonably likely to adversely affect the registrant's ability to record,
     process, summarize and report financial information; and

          b) Any fraud, whether or not material, that involves management or
     other employees who have a significant role in the registrant's internal
     control over financial reporting.

Date: March 11, 2004

                                          By:      /s/ W. BLAKE BAIRD
                                            ------------------------------------
                                                       W. Blake Baird
                                                   President and Director
                                              of AMB Property Corporation, the
                                              general partner of AMB Property,
                                                             L.P.
<PAGE>

I, Michael A. Coke, certify that:

     (1) I have reviewed this annual report on Form 10-K of AMB Property, L.P.;

     (2) Based on my knowledge, this report does not contain any untrue
statement of a material fact or omit to state a material fact necessary to make
the statements made, in light of the circumstances under which such statements
were made, not misleading with respect to the period covered by this report;

     (3) Based on my knowledge, the financial statements, and other financial
information included in this report, fairly present in all material respects the
financial condition, results of operations and cash flows of the registrant as
of, and for, the periods presented in this report;

     (4) The registrant's other certifying officers and I are responsible for
establishing and maintaining disclosure controls and procedures (as defined in
Exchange Act Rules 13a-15(e) and 15d-15(e)) for the registrant and have:

          a) Designed such disclosure controls and procedures, or caused such
     disclosure controls and procedures to be designed under our supervision, to
     ensure that material information relating to the registrant, including its
     consolidated subsidiaries, is made known to us by others within those
     entities, particularly during the period in which this report is being
     prepared;

          b) Evaluated the effectiveness of the registrant's disclosure controls
     and procedures and presented in this report our conclusions about the
     effectiveness of the disclosure controls and procedures, as of the end of
     the period covered by this report based on such evaluation; and

          c) Disclosed in this report any change in the registrant's internal
     control over financial reporting that occurred during the registrant's most
     recent fiscal quarter (the registrant's fourth fiscal quarter in the case
     of an annual report) that has materially affected, or is reasonably likely
     to materially affect, the registrant's internal control over financial
     reporting; and

     (5) The registrant's other certifying officers and I have disclosed, based
on our most recent evaluation of internal control over financial reporting, to
the registrant's auditors and the audit committee of the registrant's board of
directors of the registrant's general partner (or persons performing the
equivalent functions):

          a) All significant deficiencies and material weaknesses in the design
     or operation of internal control over financial reporting which are
     reasonably likely to adversely affect the registrant's ability to record,
     process, summarize and report financial information; and

          b) Any fraud, whether or not material, that involves management or
     other employees who have a significant role in the registrant's internal
     control over financial reporting.

                                          By:      /s/ MICHAEL A. COKE
                                            ------------------------------------
                                                      Michael A. Coke
                                                Chief Financial Officer and
                                              Executive Vice President of AMB
                                                           Property
                                            Corporation, the general partner of
                                                             AMB
                                                       Property, L.P.

Date: March 11, 2004