The Browns also waived fellow quarterback Tyler Thigpen.
Grossman, 33, worked out for the Miami Dolphins on Monday, with the Dolphins electing to sign Brady Quinn instead. Grossman spent the last four years with the Washington Redskins. He hasn't played in the regular season since he started 13 games for Washington in 2011, serving as the team's emergency third quarterback the past two seasons.
In his 11 NFL seasons, Grossman has thrown for 10,232 yards, 56 touchdowns and 60 interceptions. He quarterbacked the Chicago Bears during their run to Super Bowl XLI following the 2006 season.
Thigpen, 30, spent the past two seasons with the Buffalo Bills before joining the Browns. He last started a game in 2010, for the Dolphins.
In the Browns' latest depth chart, Thigpen had been listed third-string at quarterback.
- Ben Estes