Edwards got hurt in Sunday's loss at Cincinnati. He returned two punts for 14 yards and had one carry for no gain before getting injured. Edwards played in two games for Cleveland after being signed on Oct. 30.
The 5-foot-9, 190-pound Cooper spent the first four weeks of the season on the Browns' active roster. He spent the past six weeks on the practice squad.
The Browns signed wide receiver Reggie Dunn to the practice squad.