The 27-year-old right-hander, who became a free agent last month when Detroit failed to offer a 2016 contract, is 15-12 with a 3.17 ERA and 97 saves in 246 big league appearances.
He was 1-2 with a 4.58 ERA in 18 appearances for the Rangers last year, became a free agent in July after he was designated for assignment, then signed Detroit last July and went 2-2 with a career-worst 7.62 ERA in 28 1/3 innings.
Feliz was the Rookie of the Year with Texas in 2010, when he was an AL All-Star and had 40 saves. He had Tommy John surgery is 2012.
Feliz can earn $300,000 in bonuses for relief appearances: $30,000 for 40 and each additional four through 76. He also can make $250,000 for games finished: $50,000 each for 35 and each additional five through 55.