The 35-year-old Grossman was signed last week and was unimpressive, completing 4 of 9 passes for 41 yards, in Thursday night's preseason win over Baltimore. Grossman played for the Chicago Bears for six years and also spent time with the Texans and Redskins.
Yates was Ryan's top backup in 2014.
The Falcons also released defensive end Cliff Matthews, a seventh-round pick in 2011.
The cuts left the Falcons with 67 players. NFL teams must reduce rosters to 53 players by Saturday.
AP NFL websites: http://www.pro32.ap.org and http://www.twitter.com/AP-NFL