The 32-year-old Jeffress can earn $200,000 in performance bonuses: $50,000 each for 40, 45, 50 and 55 games pitched.
Jeffress was one of baseball's most dominant relievers in 2018, going 8-1 with a 1.29 ERA and 15 saves in 73 games for Milwaukee. But the right-hander struggled with injuries last season before he was cut by the Brewers on Sept. 1.
He finished 2019 with a 3-4 record and a 5.02 ERA in 48 games.
Jeffress was selected by Milwaukee in the first round of the 2006 amateur draft and made his big league debut with the Brewers in 2010. He is 28-11 with a 3.16 ERA and 44 saves in 392 career games with Milwaukee, Texas, Kansas City and Toronto.