Gruden met with Redskins officials Wednesday and was introduced at a news conference Thursday as the ninth coach of the team since Dan Snyder bought the franchise in 1999.
Gruden replaces Mike Shanahan, who was fired the day after the Redskins' 2013 season ended with an eighth-consecutive loss and 3-13 record overall. Shanahan was 24-40 in four seasons leading Washington.
"I look forward to the challenge," Gruden said at the news conference.
"I don't know what happened last year and I don't care what happened last year," Gruden added regarding the reported dysfunction within the Redskins' organization. "I am only concerned about the future."
Gruden, 46, led the Bengals' offense from 2011-13. He had been interviewed by at least three NFL teams with head coaching vacancies last season and was in conversations with at least two in 2014 when he took the Redskins position.
Gruden has previous head coaching experience in the Arena League where he led the Orlando Predators and Florida Tuskers. He was on four Arena Bowl-winning teams as a quarterback and two as a coach.
Gruden is the brother for former Oakland and Tampa Bay Coach Jon Gruden, who is a commentator on "Monday Night Football." Jay Gruden was on his brother's staff in Tampa Bay from 2002-08.