Grossman, 29, was with Houston last season, as were new Washington offensive coordinator Kyle Shanahan and quarterbacks coach Matt LaFleur.
The Redskins announced Grossman's signing to a one-year agreement Wednesday.
Grossman spent six seasons with the Bears before joining the Texans for one year. He's appeared in 37 games, starting 31, and completed 524-of-971 passed for 6,197 yards, 33 touchdowns and 36 interceptions.
He was the starting quarterback in 2006 when the Bears were an NFC-best 13-3 and advanced to Super Bowl XLI against the Indianapolis Colts.
Washington recently released long-time backup quarterback Todd Collins.
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