Fultz, 34, had been released by Cleveland on Friday after going 0-1 with an 11.88 ERA in seven games for the Indians during Grapefruit League play. In 8 1/3 innings, Fultz gave up 11 earned runs on 16 hits and three walks.
Fultz went 4-3 with a 2.92 ERA in 49 games for the Indians in 2007, though he was sidelined for a couple of weeks due to a strained muscle in his side.
Fultz provides some insurance in case the Tigers, who start the season with two relievers on the disabled list and perhaps a third on the restricted list, need another lefty reliever. Bobby Seay is the only lefty reliever expected to open the season with Detroit.
Fultz is 25-15 with a 4.26 ERA in an eight-year career with the Phillies, Twins, Rangers, Giants and Indians.
Jim Molony is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.