The deal will be for $4.5 million over two years.
Perez resurrected his career in Seattle as a reliever after a tough time starting with the Mets following a $36 million, three-year deal.
Perez will provide a needed lefty for Arizona's bullpen. Several other teams, mostly in the National League, expressed interest. The Marlins and Braves were believed to be among them.
Ken Rosenthal of Foxsports.com first said a deal was close.