Along with Garza, the Cubs received outfielder Fernando Perez and minor league pitcher Zachary Rosscup.
In return, the Rays got five minor leaguers from the Cubs, including pitcher Chris Archer, catcher Robinson Chirinos, infielder Hak-Ju Lee and outfielders Sam Fuld and Brandon Guyer.
Garza, 27, compiled a 15-10 record with a 3.91 earned-run average in 33 games last season for the Rays. He tossed a no-hitter in July and sports a career mark of 42-44 with a 3.97 ERA over five years with Tampa Bay and Minnesota.
Perez batted .234 in 41 games last season for the Rays.