Clayborn, 31, appeared in 15 games (one start) with the Atlanta Falcons in 2019. He recorded 18 total tackles, four sacks and two forced fumbles as a situational pass-rusher last season.
The Browns were actively searching for an experienced pass-rusher this off-season, according to ESPN. Clayborn, entering his 10th season in the league, is expected to play opposite All-Pro edge rusher Myles Garrett in 2020.
The Tampa Bay Buccaneers selected Clayborn in the first round of the 2011 NFL Draft out of Iowa. He spent his first four seasons in Tampa before joining the Falcons for the first time in 2015.
Clayborn played three seasons with the Falcons and recorded a career-best 9.5 sacks in the 2017 campaign before signing with the New England Patriots in March 2018. After one season in New England, he rejoined the Falcons for a second stint in 2019.
In 110 career games between the Buccaneers, Falcons and Patriots, Clayborn has notched 196 total tackles, 36.5 sacks and one pass defensed.