The deal completed Monday night gives the Rangers a boost to a starting rotation plagued by injuries.
Texas sent the Cubs rookie pitcher Justin Grimm, top prospect third baseman Mike Olt and Class-A pitcher C.J. Edwards. There will also be a player to be named later.
Garza, a 29-year-old right-hander who can be a free agent after the season, is 5-0 with a 1.24 ERA his last six starts.
He had been scheduled to start Monday night for the Cubs in Chicago.