Jaye's contract was purchased from Triple-A Toledo on Friday.
Jaye pitched well after moving up to Toledo last season, sporting a 3.69 ERA after seven starts, so the Tigers decided to reward him with a spot on the 40-man roster. Detroit has a plethora of starters that are major-league ready, so the 24-year-old's will likely continue to develop at Triple-A unless he makes the switch to the bullpen.