To make room for him on the roster, the club designated outfielder Greg Golson for assignment. The club has 10 days to trade, release or outright Golson to the minors.
The Rangers still have not made a corresponding move to put RHP Colby Lewis on the 40-man roster.
Greene, 30, played in 77 games with the Cardinals in 2009, hitting .200 with six homers and 24 RBIs. He spent two stints on the disabled list dealing with social anxiety disorder. He was limited by a broken left hand for part of 2008 with San Diego after punching a storage chest near the dugout.
Greene believes he's in a better place in regard to his personal issues, and said he enjoyed playing the game again when he came of the disabled list the second time in 2009.
"I feel like at that point, it was something that was lingering as far as having unresolved personal things," Greene said in a conference call Thursday. "I won't get into specifics, but I don't think it's any different than a lot of people as far as stresses and pressure of everyday life on the field and off the field. I was carrying that on the field where the game itself becomes an obstacle. It wasn't the primary obstacle, but it was difficult."
Greene said that once he took a proactive role in why he felt that way and why, his frustration level was so high that things got better.
"When I came back after that [second time on DL], I felt reborn as a player," Greene said. "I felt like I was able to enjoy what I was doing."
The Rangers' role for Greene is to be able to play every infield position, mainly shortstop and third base. Manager Ron Washington said Greene would also take ground balls at second and first in spring training so he could try to learn those positions and play them if necessary.
Greene played his best season in the majors in 2007 as the Padres' primary shortstop. He hit .254 with 27 homers and 97 RBIs and was named the team's MVP as the club barely missed the playoffs.
Greene was taken in the first round of the 2002 draft and was second in the 2004 National League Rookie of the Year voting (behind Pittsburgh's Jason Bay).
Since the start of the 2004 campaign, Greene is fifth among major league shortstops with 84 homers and is seventh with 332 RBIs. He has a career average of .245 in 736 games with San Diego and St. Louis.
Golson, 24, played most of the 2009 season in Triple-A Oklahoma City. He hit .258 with two homers, 17 doubles, eight triples and 40 RBIs in 123 games. He was 20-for-24 in stolen base attempts. Golson was acquired for John Mayberry Jr. in a trade with Philadelphia before last season.