McClain, 29, spent the 2017 season with Washington. He recorded 20 tackles and two sacks in 12 games, starting just two contests after being passed up on the depth chart by Stacy McGee. Washington released McClain in April after selecting defensive linemen Da'Ron Payne and Tim Settle in the NFL draft.
The Falcons are McClain's sixth NFL team. He previously played for the Carolina Panthers, New England Patriots, Houston Texans, Dallas Cowboys and Washington. Primarily a backup throughout his career, McClain recorded a career-high 39 tackles and 2.5 sacks while starting 15 games in 2016.
McClain has 75 tackles and 6.5 sacks for his career.
He'll likely compete with Jack Crawford for a starting job alongside Grady Jarrett in the middle of the defensive line. It's needed depth after Dontari Poe left to sign with the Carolina Panthers.