Teague was taken with the 29th selection out of Kentucky and is expected to fill a backup role at point guard. The Bulls signed Kirk Hinrich and Nate Robinson in an effort to get by while Derrick Rose recovers from a major knee injury.
Teague averaged 10.0 points and 4.8 assists to help Kentucky win a national title in his lone season. Older brother Jeff plays for Atlanta.
The Bulls announced the deal Wednesday.