Gagne, 30, is a right-hander who has spent the past eight seasons with the Los Angeles Dodgers. He was the 2003 Cy Young winner who has been limited to 16 games over the past two years because of back and elbow surgery. He had 158 saves between 2002-04.
Although the Rangers are deep with young relievers, club officials view Gagne as one of the few free agents left on the market who could make a serious impact on a team. He could be an eighth-inning setup reliever or he could take over as closer. That would allow the Rangers to use Akinori Otsuka in the eighth inning.
The Rangers also view Gagne as a mentor to their young relievers.
Gagne is the second free agent the Rangers have come to terms with in the past two days. The club officially signed center fielder Kenny Lofton to a one-year deal on Tuesday.
The Rangers also spent Tuesday meeting with free agent pitcher Mark Mulder, who is also being pursued by the Arizona Diamondbacks.
T.R. Sullivan is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.