Gruden, the younger brother of Super Bowl-winning coach Jon Gruden, replaces Mike Shanahan, who was fired the day after the Redskins finished the 2013 season with the second worst record in the National Football League.
Gruden spent the last three seasons with the Bengals where he groomed quarterback Andy Dalton.
He will now have the task of working with Robert Griffin III, who struggled in his sophomore season after capturing NFL rookie of the year honors for the 2012 campaign.
The Redskins have scheduled a news conference for 4 p.m. ET (2100 GMT) where they will introduce their eighth head coach in the last 16 seasons.
Shanahan, who had guided the Denver Broncos to two Super Bowl titles, was unable to work his magic during four seasons at the helm in Washington. He led the team to the playoffs once while posting a 24-40 record.
The Redskins closed out the 2013 season with an eight-game losing skid.