Martin, who hit .172 in 49 games last season with the Seattle Mariners and the Chicago Cubs, can earn $1.25 million in performance bonuses based on plate appearances. He would receive the full amount at 500 plate appearances.
The Tigers also announced Tuesday that they have signed right-hander Enrique Burgos, catcher Derek Norris, first baseman Edwin Espinal and outfielder Jim Adduci to minor league contracts for 2018, with invitations to major league spring training.
In September, Norris was suspended for the remainder of the season by Major League Baseball for violating the sport's domestic violence policy nearly two years earlier. He was a free agent when he was suspended, having been released by the Tampa Bay Rays in late June.