The 33-year-old Grossman is entering his 12th year in the NFL and joins a team where Brian Hoyer and Johnny Manziel are vying for the starting job. He hasn't played in the regular season since 2011, when he started 13 games for Washington.
Grossman, a former first-round pick, has played for the Bears (2003-08), Texans (2009) and Redskins (2010-13). In the 2006 season, he led Chicago to the Super Bowl in his first full season as the starter.
Grossman has gone 25-22 as a starting quarterback. He has completed 863 of 1,562 passes for 10,232 yards with 56 touchdowns and 60 interceptions.