Clowney inked a one-year contract worth up to $10 million after he passed his physical, sources told Ian Rapoport of NFL Network.
"Jadeveon's had a very productive career since 2014. We love his relentless style of play," Browns general manager Andrew Berry said. "He's one of the more disruptive players in the game and we think he's going to add an element of ruggedness along our defensive line and will pair nicely with many of the guys we have on the roster already."
Cleveland pursued the 2014 No. 1 pick last offseason, but the Browns lost out to the Tennessee Titans despite reportedly making the largest offer of his suitors.
Clowney first met with the AFC North club in late March, leaving the visit without a deal. He then met again with the Browns on Wednesday.
The former Houston Texans standout has struggled in recent seasons. Clowney registered just one sack with the Seattle Seahawks in 2019, and none over eight games with the Titans last season.
He racked up 29 sacks and made three Pro Bowls during his five years in Houston.