Garza, who became the first member of the Rays to pitch a no-hitter when he blanked the Detroit Tigers last season, was the centerpiece of the eight player deal that also saw outfielder Fernando Perez and left-handed pitcher Zachary Rosscup move to Chicago.
Headed to Tampa are prospects right-handed pitcher Chris Archer, catcher Robinson Chirinos, infielder Hak-Ju Lee and outfielders Sam Fuld and Brandon Guyer.
"It's not every day a premier and proven big-game pitcher entering his prime becomes available, and we couldn't be more thrilled to add Matt Garza to our pitching staff," Cubs general manager Jim Hendry said in a statement.
"It is impossible to acquire a pitcher of Matt's caliber and not give up some quality talent and Tampa Bay certainly is acquiring solid prospects in this deal.
"But Matt brings a tremendous arm to help solidify a formidable pitching rotation not only for 2011 but for many years to come."
Garza posted a record of 15-10 last season with a 3.91 ERA and is 34-31 in 95 big-league appearances over the last three years but is also a proven post-season performer.
(Writing by Steve Keating in Indianapolis; editing by Steve Ginsburg)