Goudeau signed a minor-league contract with the Tigers on Tuesday and received an invitation to major-league spring training.
Goudeau put up a 7.08 ERA and a 1.72 WHIP through 20.1 major-league innings with Colorado last season, and his minor-league stats weren't outstanding either with a 9.51 ERA and 1.93 WHIP over 64.1 frames. The 30-year-old reliever will spend spring with the big-league club, but will almost certainly serve as organizational depth in Triple-A.