Cook played 16 games for the Houston Rockets this season before being released Thursday. He averaged 3.4 points in 10.3 minutes.
Cook was the 21st pick in the 2007 draft out of Ohio State by the Philadelphia 76ers before being traded to the Miami Heat. He has also played for the Oklahoma City Thunder.
The 6-foot-5 Cook won the 3-point contest at All-Star weekend in 2009. He has averaged 6.9 points for his career.
Chicago announced the signing Sunday.
Bulls coach Tom Thibodeau addressed the reality of the veteran officially joining the Bulls roster on Sunday.
“Right now, we’re pretty much set with our rotation,” Thibodeau said.
The Bulls added Cook for numerous reasons, none of them immediate. He’ll sit on the bench for Monday’s game against the Cavaliers as he learns the system and his teammates.