Thompson originally was a third-round choice of the Bengals in 2012. He spent four seasons in Cincinnati, making 53 tackles and three sacks in 39 games.
He missed all of 2016 while recovering after tearing an anterior cruciate ligament at the end of the 2015 season. The Bengals cut Thompson two days ago.
PFT reported Bryant’s release earlier Tuesday night before the team announced the transaction and thanked him for his time in Cleveland.
“We’d like to thank Des for all his contributions to the Cleveland Browns in his time with our organization,” said Sashi Brown, the Browns executive vice president of football operations. “He proved to be a leader and tone-setter along our defensive front, and we wish him well.”
Bryant joined the Browns as an unrestricted free agent in 2013, starting 41 games in his career in Cleveland. He missed all of the 2016 season after tearing a pectoral muscle.