The deal came Tuesday night. The Indians are working on other deals, including one that could include shortstop Asdrubal Cabrera.
Choo, who has been Cleveland's primary right fielder for the Indians since 2006, will likely play centre and bat leadoff for Cincinnati.
Dealing Choo was almost a necessity for the Indians. He was entering the final year of his contract and is eligible for free agency in 2013. The Indians have not been able to work out a deal with agent Scott Boras, who has turned down several extensions in recent years.
The 30-year-old Choo batted .283 with 16 homers and 67 RBIs in 155 games last season. Donald hit .202 in 43 games.
Stubbs has played centre exclusively for the Reds. He batted .213 with 14 homers and 40 RBIs, and struck out 166 times in 493 at-bats.