Bowie was a seventh-round pick a year ago and made eight starts during his first NFL season. But he needs shoulder surgery that will sideline him for four to six months, and he was cut by the Seahawks on Saturday.
The 6-foot-5, 320-pound Bowie helped clear the way for Marshawn Lynch to run for 1,257 yards and 12 touchdowns last season. He also started a playoff game in Seattle's run to the Super Bowl title.
Cleveland general manager Ray Farmer announced the waiver claim on Sunday. It brings the Browns' roster to 90 players.
The Seahawks claimed tackle Cory Brandon off waivers from Arizona to fill Bowie's spot on their roster.