The Material Transfer Agreement (MTA) must be signed by someone who is authorized to approve legal documents on behalf of your entire institution. The signatory binds your institution to the terms (and all the obligations herein) of the MTA. In the event of a breach of this agreement, your institution could be held liable.
Within the United States, these agreements are typically signed by a member of the Technology Transfer, Sponsored Research, or Legal Office. For international institutions that do not have these departments, a dean or head of department may be authorized to sign.
If you are unsure who should sign your MTA, please check with a member of your administration.