Rogers, a 10-year veteran, was released after recording 17 tackles and two sacks in 15 games last season, his third with the Browns.
He played seven seasons in Detroit previously, and for his career has racked up 482 tackles and 37.5 sacks.
Also released by the Browns Wednesday were defensive lineman Kenyon Coleman, linebackers Eric Barton and David Bowens, offensive lineman John St. Clair and tight end Robert Royal.
Coleman is a nine-year veteran with 310 career tackles; Barton has compiled 840 stops and 20 sacks during a 12-year career; and Bowens registered 298 tackles and 38.5 sacks in 12 seasons.
Royal has made 128 catches for 1,271 yards and 14 scores over a nine-year career and St. Clair's 11-year career has included 132 games.