Gorzelanny, 32, had a 0.86 earned run average while making 23 appearances out of the Milwaukee bullpen last season. He missed two-plus months recovering from offseason shoulder surgery.
"We are pleased to add a veteran pitcher like Tom to our ball club," said Tigers president, chief executive officer and general manager David Dombrowski. "Tom is an established reliever who can help solidify the bullpen on the left side and will be a nice addition to our roster."
To create room for Gorzelanny on the 40-man roster, the Tigers designated pitcher Luke Putkonen for assignment.