ESPNChicago.com's Bruce Levine reported Friday that the teams had reached agreement on the deal.
The Cubs sent 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 left-handed pitcher Zachary Rosscup.
Garza, who arrived in Chicago on Friday for his physical, sounded ready to get to work.
"I'm just happy to be a part of this long tradition," Garza said. "I'll just try to get this thing turned around in a good direction. We've got a lot of the pieces to the puzzle right there in Chicago, ready to do it."
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. Cubs general manager Jim Hendry was glad to land the power pitcher he was looking to acquire.
"You don't always pull off things the way you want to," Hendry said. "Sometimes the names change. But I will tell you that Matt Garza was a guy we targeted. I didn't know if we could do it, but that was the one [trade] that made the most sense for us."
"This was a great trade for the present and the future," Hendry said.
Garza, 27, is coming off his best season, compiling a 15-10 record with a 3.91 ERA. Garza averaged 6.6 strikeouts and 2.77 walks per nine innings and pitched a no-hitter against the Detroit Tigers. Hitters batted .248 against Garza in 2010.
He spent his first two major league seasons with the Minnesota Twins and the past three with the Rays. Garza, who won two games in the AL Championship Series in 2008 when the Rays advanced to the World Series, joins a rotation that already includes Carlos Zambrano and Ryan Dempster.
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.
"Simply said, we really like the deal a lot. It kind of fits in with our short-term and long-term objectives," Rays executive vice president of baseball operations Andrew Friedman said. "It's a perfect win-win trade for both sides or we wouldn't have done it."
Archer, 22, combined to go 15-3 with 2.34 in 28 games between Class A Daytona and Double-A 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 Tennessee in 2010. The 24-year-old was the Cubs' minor league player of the year.
Fuld played in 98 games for the Cubs between 2007 and 2010. He batted .299 in 65 games in '09.
Lee, who batted .282 at Class A Peoria last season, originally signed with the Cubs as a non-drafted free agent on March 29, 2008. The Cubs already have a young shortstop for their future in Starlin Castro.
Garza made $3.35 million last season. Pena earlier agreed to a $10 million, one-year contract with the Cubs. Others who departed Tampa Bay include outfielder Carl Crawford, who received a $142 million, seven-year contract from Boston, and reliever Joaquin Benoit, who got a $16.5 million, three-year deal with Detroit.
"It's a shame that it's got to be like that, but it's the nature of the beast," Garza said of the exodus from Tampa. "It's the way this game works."
Information from ESPNChicago.com's Bruce Levine and The Associated Press was used in this report.