Detroit would have had to pay a $500,000 buyout if it had declined the option on the 30-year-old right-hander, who was acquired from Texas in July.
Soria had 17 saves for the Rangers, then strained an oblique in August and pitched only 11 innings for the Tigers in the regular season. Soria gave up Delmon Young's go-ahead, three-run triple in the eighth inning of the Game 2 loss to Baltimore in the AL Division Series.
Detroit also made $15.3 million qualifying offers to right-hander Max Scherzer and designated hitter Victor Martinez, well ahead of Monday's deadline. Detroit would receive draft-pick compensation if either of those free agent stars signs with another major league team before the amateur draft in June.
Detroit sent right-hander Evan Reed and utilityman Don Kelly to Triple-A Toledo. Outfielder Andy Dirks, who missed this entire season because of a back issue, was claimed off waivers by the Toronto Blue Jays, and left-hander Patrick McCoy was claimed off waivers by the Baltimore Orioles.
The Tigers also selected the contract of outfielder Wynton Bernard from Class A West Michigan.