Although many expected the Redskins to sign former Broncos quarterback Chris Simms, Washington made a different move at the position.
The Redskins reached agreement Wednesday with former Bears and Texans quarterback Rex Grossman on a one-year deal, the team announced.
The deal reunites Grossman, 29, with Redskins offensive coordinator Kyle Shanahan, who also spent last season in Houston.
"Rex has some experience with Kyle Shanahan in Houston," Redskins general manager Bruce Allen said. "He wanted to give us an opportunity, and we're glad to give him one."
Allen deflected a question whether Grossman would be a backup in Washington or get a chance to compete for the starting QB job, saying: "We're going to continue to try and add competition for every position."
Grossman, who has thrown for 6,197 yards, 33 touchdowns and 36 interceptions, led the Chicago Bears to the 2007 Super Bowl.
He played in only 12 games the next two seasons, and left the Bears as a free agent in 2009.
Grossman has played in 37 NFL games, including 31 starts. He has completed 524 of 971 passes (54 percent).
"We want competition," Mike Shananan said. "As you look at Rex's background, you can see what he's done, the experience he has. He, obviously, has a year into the system. I'm looking forward to seeing all these quarterbacks -- what they can do on the field."
The Redskins released veteran backup quarterback Todd Collins on March 4.
Adam Schefter is ESPN's NFL Insider. Information from The Associated Press was used in this report.