The deal is worth $2.75 million. It will pay him $2.5 million in 2019 and includes a $250,000 buyout on a $2.5 million option for 2020.
Kelley, 34, posted a 2.94 ERA last season in stints with the Washington Nationals and Oakland Athletics, who acquired him in August. Kelley was designated for assignment by the Nationals on Aug. 1 after throwing a tantrum on the mound following a home run and was traded to the A's on Aug. 5.
The right-hander shook off a dreadful 2017 to look like his typical self in 2018, when he struck out 50 in 49 innings and walked just 11.
Kelley is the second addition to the bullpen for the Rangers, who have been among the busiest teams in free agency, signing reliever Jesse Chavez, as well as starters Lance Lynn and Shelby Miller, infielder Asdrubal Cabrera and catcher Jeff Mathis.