The 32-year-old right-hander has a 3.23 ERA in six major league seasons, the past four with Detroit. He had attended spring training with Cleveland and opted out of his deal after being told he would not make the opening-day major league roster.
Brewers closer Corey Knebel is out indefinitely with a partial tear of the ulnar collateral ligament in his right elbow, the type of injury that sometimes ends in Tommy John surgery. He's expected to join Jeremy Jeffress, down with a sore right shoulder, on the injured list to open the season.
Milwaukee announced the deal Sunday.