Walters, who was outrighted off the 40-man roster on Oct. 24, made 12 starts with the Twins in 2012, posting a 5.69 ERA with 42 strikeouts and 22 walks in 61 2/3 innings. He was signed before the season as a Minor League free agent.
The 27-year-old has a career 6.39 ERA over parts of four seasons with the Cardinals, Blue Jays and Twins. He has struck out 82 and walked 44 in 112 2/3 innings.
Walters figures to compete to be a starter next season, as left-hander Scott Diamond is the only pitcher who is guaranteed a spot in the rotation.