Agent Brian Overstreet told ESPN's Josina Anderson that Griffin will join Washington with a one-year deal worth $2.5 million.
Griffin was cut last week by Minnesota, where he played for six seasons. He came back after tearing the ACL in both knees in 2010 to play in all 16 games last year, but he wasn't able to regain his previous form, was benched late in the season and expressed dissatisfaction with his demotion.
He had three years left on his contract when he was released by the Vikings and had been due $4.1 million in salary for 2012.
The Redskins also announced that tight end Fred Davis has signed his franchise player tender, a one-year deal worth $5.446 million. General manager Bruce Allen has said he hopes to sign Davis to a long-term contract.
Information from The Associated Press was used in this report.