In the transaction, the Indians shipped Choo, infielder Jason Donald and approximately $3.5 million to the Reds while also sending reliever Tony Sipp and first baseman Lars Anderson to the Arizona Diamondbacks.
The Tribe in return received pitchers Trevor Bauer, Matt Albers and Bryan Shaw from the Diamondbacks and outfielder Drew Stubbs from the Reds.
Minor-league infielder Didi Gregorius went from Cincinnati to Arizona as part of the deal.
Choo, an eight-year veteran, batted .283, hit 16 homers and drove in 67 runs over 155 games with the Indians last season. He will likely replace Stubbs in the Reds' outfield.
Stubbs batted .213 with 14 homers and 40 RBIs in 136 games last season.
The 21-year-old Bauer, meanwhile, was the third-overall draft choice in 2011 draft and was named the Diamondbacks' Minor League Pitcher of the Year thanks to a 12-2 record with a 2.42 ERA in 22 combined starts for Class A Reno and Class AA Mobile.