The Cubs acquired Triple-A infielder Mike Olt, Class A right-hander C.J. Edwards and right-hander Justin Grimm from the Rangers. The Cubs also will receive one or two players to be named later, depending on who they take, as part of the deal.
Garza was flying to the Dallas/Fort Worth area Monday night and will work out with the Rangers on Tuesday. Texas general manager Jon Daniels said Garza is likely to start Wednesday night against the New York Yankees.
"He's an extremely talented pitcher," Daniels said. "He's had success in the toughest divisions and the biggest stages. He was throwing the ball as well as anybody right now. He has a power repertoire, who is something that's a little different from what we've got. And he was available.
"He was in our opinion the best guy on the market, and we wanted to go out and make a push to get him."
Fox Sports first reported the trade.
The 29-year-old Garza is 6-1 with a 3.17 ERA overall this season, including 5-0 with a 1.24 ERA in his past six starts. He is entering the final year of his contract.
"He was the best pitcher in baseball in his last five, six, seven starts. He's young, has great velocity, has good command of his pitches and that makes him attractive to any team," Cubs manager Dale Sveum said. "It's not easy to part with a guy like Garza and someone has to step in and be productive. We hope the players we get will make us a better team, and in the future, we can be the team who pursues a player like Garza."
The Rangers have long had interest in Garza, going back to when he signed as a free agent with the Cubs in 2011. Garza has struggled at Rangers Ballpark in Arlington, where he is 2-3 with a 6.04 ERA in five starts. Garza did beat the Rangers in Arlington in Game 3 of the 2010 American League Division Series when he was with the Tampa Bay Rays, allowing an earned run in six innings in a 6-3 victory.
The deal came together with the Cubs sifting through several top prospects the Rangers have in the lower minor leagues. The Cubs wanted pitchers Martin Perez and Luke Jackson, but the Rangers balked with Garza essentially being a rental player in the last year of his contract.
"We certainly had interest in him," Rangers CEO Nolan Ryan said Monday.
With six pitchers currently on the disabled list, including four starters, Texas has been in the market for a starting pitcher for weeks. The Rangers are in a heated division race with Oakland, trailing the A's by three games in the AL West entering Monday night.
Staff ace Yu Darvish came off the 15-day disabled list and started Monday night against the Yankees, earning the win. He took Grimm's spot on the 25-man roster. Fellow right-hander Alexi Ogando will come off the DL on Tuesday.
Grimm was 7-7 with a 6.37 ERA in 17 starts this season. His last start was July 12 at Detroit, when he allowed 10 hits and seven runs over 3 1-3 innings before leaving with soreness in his right forearm.
Olt, a 24-year-old corner infielder, was hitting .213 with 11 home runs and 32 RBIs in 65 games for Triple-A Round Rock this year. Entering the season, ESPN Insider Keith Law ranked Olt as the 71st-best prospect in baseball and second overall for the Rangers. He was a supplemental first-round pick in the 2010 draft.
Olt played in 16 games for the Rangers at the end of last season. But the Rangers have Gold Glove-winning third baseman Adrian Beltre under contract through 2016.
The 21-year-old Edwards, who made his pro debut with 20 scoreless innings in the Arizona League last year, is 8-2 with a 1.83 ERA and 122 strikeouts in 93 1-3 innings for Class-A Hickory. He hasn't allowed a home run in 160 1-3 professional innings.
"We felt real good about the players we got back," Cubs general manager Jed Hoyer said. "Mike Olt is a player we tried to get last year. He has had a little bit of a down year; that is sometimes the best time to get a player. We hope he can return to form of last year. He has power and is a good defender. Edwards is a player we scouted extensively. He really stuck out with a great fastball and has really come into his own this year. Justin Grimn is a guy who pitched well last year and ended up in the big leagues. He is a guy we think has a great future. He has a real good fastball and curve ball combination."
Olt and Grimm will report to Triple-A Iowa. Edwards will join the Cubs' Class A affiliate in Daytona.
Information from ESPNChicago.com's Bruce Levine, ESPNDallas.com's Todd Wills, ESPN's Jim Bowden and The Associated Press was used in this report.