Pending a physical, Hensley will reportedly make a base salary of $750,000, but he could earn as much as $300,000 in incentives and awards.
Spending six seasons in the National League with the Padres and Marlins, Hensley has a career 24-29 record with a 3.94 ERA. The 32-year-old right-hander become a free agent in December when he was non-tendered by Miami.
He'll join a bullpen that includes Javier Lopez, Santiago Casilla, Sergio Romo, Jeremy Affeldt and Brian Wilson.
Hensley may best be known for giving up Barry Bonds' 755th home run, which tied Bonds with Hank Aaron for first on the all-time list.
Quinn Roberts is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.