Gutierrez joins the bank from Global Political Strategies, where he worked as chairman of the communications firm.
He was commerce secretary from 2005 to 2009 under Bush. Gutierrez previously spent three decades with Kellogg Co
Gutierrez is the latest hire in a push by the third largest U.S. bank by assets to add executives from inside the nation's capital.
On Tuesday, Bloomberg reported the bank was in advanced talks to hire former U.S. budget director Peter Orszag.
Orszag left U.S. President Barack Obama's administration in July, and currently is at the Council on Foreign Relations think tank.
(Reporting by Joe Rauch; Editing by Tim Dobbyn)