The 30-year-old Clayborn spent three seasons in Atlanta from 2015 to 2017 before joining the New England Patriots in 2018. He had 11 tackles, 2.5 sacks and one forced fumble in the Patriots' defensive line rotation.
The Tampa Bay Buccaneers originally drafted Clayborn in the first round of the 2011 NFL Draft out of Iowa. He spent his first four NFL seasons with the Bucs before switching to the Falcons.
The Falcons had a need on the defensive line this off-season and recently hosted former New Orleans Saints defensive tackle Tyeler Davison for a free-agent visit.
In Clayborn's eight NFL seasons, he has appeared in 95 games with 41 starts. He has recorded 178 total tackles, 32.5 sacks, 90 quarterback hits and eight forced fumbles.
Clayborn registered 17 quarterback hits and a career-high 9.5 sacks in the 2017 season, including a franchise-record six sacks against the Dallas Cowboys in Week 10.