The team announced the decision on Monday. Baker didn't pitch this year because of an elbow injury that required elbow-ligament replacement surgery. The Twins have expressed interest in bringing him back for 2013, but not at that price.
The 31-year-old Baker was a second-round draft pick by the Twins in 2003. He is 63-48 with a 4.15 ERA since his debut in 2005, spanning 163 appearances and 159 starts.
The Twins also agreed to terms with right-hander P.J. Walters on a minor league contract with an invitation to spring training. Walters went 2-5 with a 5.69 ERA in 12 starts last season.