Terms of the contract were not announced but NFL.com reported the fully guaranteed deal to be worth $21.1 million over four years. The team has an option for a fifth season.
On his Twitter account, Griffin said: "Well people....It's Time to go to Work!!! Off the unemployment line and oh yea HTTR!!!" The HTTR stands for Hail to the Redskins.
Griffin, 22, played three seasons at Baylor and won the 2011 Heisman Trophy as the best collegiate player as a junior. Over his career, Griffin amassed 12,644 all-purpose yards, including 10,366 passing, 2,254 rushing and 24 receiving.
Head coach Mike Shanahan has already said Griffin, known as RG3, will start when the Redskins open the 2012 National Football League (NFL) regular season at New Orleans on Sept. 9.
The Redskins were 5-11 last season and finished last in the NFC East division.