Under the terms of the new deal, Shanahan will team with Redskins executive vice president and general manager Bruce Allen, but Shanahan will have the ultimate authority on football decisions.
Shanahan will appear at a 2 p.m. ET news conference Wednesday.
As the contract was being signed at the Redskins' training complex, Shanahan and team owner Dan Snyder posed together for a picture. Then, with the deal signed, Shanahan, his agent Sandy Montag, Allen and Snyder headed out for a celebration dinner.
Shanahan's contract is worth approximately $7 million a year, the Denver Post reported on its Web site. Now that Shanahan has been hired elsewhere, the Denver Broncos, who fired Shanahan one year ago, will recoup $7 million in offset money over the next two seasons under the terms of the agreement they had with the coach.
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The Redskins' intense courtship of Shanahan began shortly after Jim Zorn was fired on Monday morning. Zorn was dismissed during a meeting in his office with Allen after the team's cross-country flight following a 23-20 loss to the San Diego Chargers on Sunday. The Redskins finished 4-12.
Allen had interviewed Shanahan via phone Monday morning, a source close to the situation told ESPN NFL Insider Adam Schefter. The Redskins and Shanahan reportedly began talks last month, a day after Allen was hired.
Shanahan won two Super Bowls in 14 seasons with the Broncos. He was fired a year ago after Denver missed the playoffs for the third straight season.
One of Shanahan's first orders of business will be assembling a coaching staff, but first he will interview Washington's assistant coaches to see which ones he would like to retain. Once those coaches are interviewed, Shanahan will launch his search for the best and brightest.
Shanahan's son, former Houston Texans offensive coordinator Kyle Shanahan, will be the Redskins new offensive coordinator.
Zorn was 12-20 over two seasons and lost 18 of his last 24 games after a 6-2 start in 2008. The Redskins struggled early this season despite a weak schedule and finished with their worst record since 1994.
"The status quo has to end," Allen said. "We have to change the way we've been doing some business. ... Last place two years in a row is not Redskins football."
Zorn's replacement will be Washington's seventh coach since Snyder bought the team in 1999. The Redskins are 82-99 on his watch, missing the playoffs in eight of 11 seasons.
"No one in the organization is satisfied with our record over the last two years," Snyder said in a statement released by the team, "and I am sure that Jim would concur with that statement. It has been painful for him, too. I certainly accept responsibility for mistakes that I have made."
Zorn's dismissal had been expected for months. The front office stripped him of his play-calling duties in late October, and Snyder interviewed assistant coach Jerry Gray for the job weeks ago, according to the Fritz Pollard Alliance, which monitors minority hiring in the NFL.
Shanahan made the playoffs in half of his 14 seasons in Denver, although he had only two losing seasons -- 6-10 in 1999 and 7-9 in 2007. His greatest successes came early, with back-to-back Super Bowl titles after the 1997 and 1998 seasons with running back Terrell Davis and quarterback John Elway.
His career regular-season record is 146-98, including 138-86 with the Broncos from 1995 to 2008 and 8-12 with the Los Angeles Raiders in 1988-89. Shanahan's playoff record is 8-5.
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