The deal, which has been agreed to pending physicals, sends right-handed pitcher Chris Archer, outfielder Brandon Guyer, catcher Robinson Chirinos, shortstop Hak-Ju Lee and outfielder Sam Fuld to Tampa for Garza, minor league outfielder Fernando Perez and another minor leaguer.
Archer, 22, combined to go 15-3 with 2.34 in 28 games between Single-A Daytona and Tennessee, and was the Cubs' 2010 minor league pitcher of the year. Archer was acquired by the Cubs in a trade that sent popular utility man Mark DeRosa to the Cleveland Indians.
Guyer batted .344 with 13 home runs and 58 RBIs for Double-A Tennessee in 2010. The 24-year old was the Cubs' minor league player of the year.
Lee batted .282 and stole 32 bases for Class A Peoria.
Fuld played in 98 games for the Cubs between 2007 and 2010. He batted .299 in 65 games in '09.
The Cubs and at least three other teams had been negotiating with the Rays for Garza since the December winter meetings in Lake Buena Vista, Fla.
Garza, 27, is coming off his best season, in which he compiled a 15-10 record with a 3.91 ERA. Garza averaged 6.6 strikeouts and 2.77 walks per nine innings. Hitters batted .248 against Garza in 2010.
Tampa, in the mode of retooling the next few seasons, was willing to trade Garza for top young talent. The Rays were looking to get a shortstop, catcher and some top-caliber young pitching in return for Garza.
Bruce Levine covers baseball for ESPNChicago.com and ESPN 1000.