In 61 games for the Dodgers in 2014, Wright was 5-4 with a 4.35 ERA and a 1.41 WHIP. He had a 3.50 ERA before the All-Star break and a 5.74 ERA afterward.
"Jamey brings a lot of experience and has contributed in a number of relief roles," general manager Jon Daniels said. "He's arguably been at his best recently, late in his career. He will compete for a spot in our bullpen."
Since the beginning of the 2008 season, Wright has made 437 relief appearances, the 10th most in the Major Leagues. His 494 relief innings are the most over the past seven campaigns.
Wright has pitched in 719 Major League games, seventh most among active pitchers, over a 19-year career that began with the Rockies in 1996. He has not been on the disabled list since sustaining a right shoulder injury with the Rangers in 2007. That was his first trip to the disabled list since '02.
"The veteran-savvy presence he brings to the table is held in high regard by those who know him and have competed against him." Rangers scouting director Josh Boyd said. "He sinks his fastball and cuts it, and he could always spin the curveball."
Wright has hit 155 batters over his career, the most by an active pitcher. A.J. Burnett is second with 132. He is tied for 17th all-time with Hall of Famer Bert Blyleven, one ahead of Don Drysdale.
The Rangers' bullpen is currently led by closer Neftali Feliz. Right-hander Tanner Scheppers is expected to be the eighth-inning setup reliever. Right-hander Shawn Tolleson should also have a spot after going 3-1 with a 2.76 ERA in 64 games for the Rangers as their most reliable reliever.
Other right-handed candidates off the 40-man roster include Phil Klein, Jon Edwards, Roman Mendez, Spencer Patton and Kyuji Fujikawa. The Rangers are also bringing Major League veterans Juan Carlos Oviedo, Ross Ohlendorf, Ross Wolf and David Martinez to camp.
The other right-handed candidate to watch is Keone Kela, a rookie who pitched in 30 games at Double-A Frisco last season and was 2-1 with a 1.86 ERA, while striking out 12.8 batters per nine innings.
T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, and follow him on Twitter @Sullivan_Ranger. This story was not subject to the approval of Major League Baseball or its clubs.