Terms of the deal weren't disclosed, but the Chicago Tribune reported it was for $5.5 million with incentive clauses that could boost the total to $7 million.
Baker, 31, missed the entire 2012 season for the Minnesota Twins while recovering from elbow ligament replacement surgery. The right-hander went 8-6 with a 3.14 ERA in 23 games in 2011.
Over 163 career games, the second-round 2003 Twins draft choice has compiled a mark of 63-48 with a 4.15 ERA.
Minnesota declined to pick up a $9.25 million option on the hurler this fall, making him a free agent.