The Heisman Trophy winner from Baylor was the second pick in this year's draft.
Griffin announced the news on Twitter: "Well people....It's Time to go to Work!!! Off the unemployment line and oh yea HTTR!!!"
The initials stand for "Hail To The Redskins," the team's fight song.
Griffin's four-year contract is worth $21.1 million and is fully guaranteed, with no offset language, a league source told ESPN NFL Insider Adam Schefter.
Of the 32 first-round draft choices, 13 remain unsigned, including top overall pick Andrew Luck.
"Offset language" is to blame for the unsigned rookie deals, although ESPN senior NFL analyst Chris Mortensen reports that was not the case in Griffin's deal.
ESPN business analyst Andrew Brandt explained the offset issue in a recent "Football Today" podcast.
"Teams want language in the contract, these are fully guaranteed contracts, saying that if they cut the player at some point and he signs with another team, they offset their guarantee," Brandt said. "So they cut a player, he signs for a million dollars somewhere, that million comes off what they owe."
Griffin will be on the field Wednesday for the third day of a five-day rookie camp. He was not considered a holdout because training camp doesn't begin officially until July 26.
Looking for a quarterback around whom to build their franchise, the Redskins made a bold offseason move, trading three first-round picks and a second-rounder to the St. Louis Rams to move into the No. 2 slot to draft Griffin.
Saying that Griffin has the ability to do things no one else has done in the NFL, coach Mike Shanahan wrapped up a rookie minicamp in May by putting Griffin squarely atop the team's depth chart.
"He's the starter. Period," Shanahan said.
The Redskins made the big move for Griffin after finishing last in the NFC East for a fourth straight season, going 5-11. It was the 16th season in the past 19 in which the Redskins didn't make the playoffs. During that span, they have started 21 quarterbacks. The most recent, Rex Grossman, committed 25 turnovers in 13 starts last season.
According to the Elias Sports Bureau, the Redskins selected three QBs in the first round since 1967 prior to drafting Griffin. In 1994, they took Heather Shuler No. 3 overall, then drafted Patrick Ramsey with the 32nd pick in 2002 and selection Jason Campbell with the 25th overall pick in 2005.
Griffin, one of the most accomplished dual-threat quarterbacks in NCAA history, set or tied 54 school records in just 41 games at Baylor before declaring for the draft.
Griffin was Baylor's career passing leader, completing 800 of 1,192 passes (67 percent) for 10,366 yards, with 78 touchdowns and 17 interceptions. His 2,254 yards and 33 TDs rushing are records for a Bears quarterback.
A few hours later, offensive lineman Josh LeRibeus, Washington's third-round choice, became the last of the Redskins' picks to sign.
Terms of the deal for the rookie from SMU were not disclosed.
Information from The Associated Press was used in this report.