McGlynn, 6-4, 320 pounds, will enter his fifth NFL season after spending previous years with the Philadelphia Eagles (2008-10) and Cincinnati Bengals (2011). He has competed in 26 career games with 18 starts.
"Mike is a tough, smart and versatile interior offensive lineman that plays hard snap to whistle," said General Manager Ryan Grigson. "We are looking forward to seeing him contribute immediately and to help set the tone for this offensive line with his aggressive style of play. He is a welcome addition to our club."
McGlynn started 14 of 16 contests for the Eagles in 2010 and blocked for a rushing attack which finished fifth in the NFL (145.3 ypg.). Philadelphia also ranked ninth in the league that season in net passing yards per game with a 244.1 average.
Last year with the Bengals, McGlynn opened rushing lanes for running back Cedric Benson who posted his third consecutive 1,000-yard season (1,067). Cincinnati's offensive line also ranked tied for fourth in the league in sacks allowed (25) as quarterback Andy Dalton became one of five rookies in NFL history to throw for 3,000-plus passing yards.