Terms of the deal were not announced.
The 6-foot-2, 302-pound McClain is expected to provide depth and experience along the interior of Atlanta's defensive line, joining Grady Jarrett, rookie Deadrin Senat, Garrison Smith and other defensive tackles on the Falcons' roster.
The 29-year-old McClain signed a four-year, $21 million contract with the Washington Redskins last season, but made only 17 tackles and two sacks in 12 games last season. He missed four consecutive games late in the season because of a toe injury. The Redskins released him on April 30.