Terms of the deal were not immediately known.
The Cavs selected Eyenga in the first round, 30th overall, in the 2009 draft, but the 21-year-old played in Spain last season to develop his skills. He averaged 3.9 points and 2.0 rebounds in 29 games for DKV Joventut Badalona.
The 6-foot-5 Eyenga played on the Cavs' Summer League team earlier this month in Las Vegas and averaged 11.4 points and 4.2 rebounds in five games.
James' departure for Miami left the Cavs with few options in free agency. The team signed Houston guard Kyle Lowry to an offer sheet that was matched by the Rockets.