Centerfielder Drew Stubbs was sent from Cincinnati to Cleveland as part of the nine-player swap.
The Diamondbacks also received shortstop prospect Didi Gregorius from Cincinnati.
Choo, who has been Cleveland's primary rightfielder since 2006, will play centerfield and bat leadoff for Cincinnati. The 30-year-old Choo batted .283 with 16 homers and 67 RBIs in 155 games last season.
The speedy Stubbs, who stole 30 bases last season, helped the Reds to NL Central titles in 2010 and 2012. -- AP