McClain agreed to a deal with the Chiefs on Tuesday, Tom Pelissero of NFL Network reports.
McClain was brought in due to multiple injuries on the Chiefs' defensive line. Starting tackle Chris Jones (groin) and reserve Xavier Williams (ankle) are both considered doubtful for Sunday's matchup against the Texans. McClain, a nine-year veteran, has been around the league during his tenure. He most recently played 13 games, including five starts, for the Falcons in 2018.