Norwood made four starts for Cleveland last season. He caught 23 passes for 268 yards and a touchdown. The former Penn State player showed he could be a potential big-play threat in Cleveland's West Coast system.
The 25-year-old Norwood will make a base salary of $465,000 this season as outlined by the collective bargaining agreement.
Norwood was originally signed by the Browns as an undrafted free agent in 2009. He was waived and spent some time on Philadelphia's practice squad before being released and re-signed by the Browns.