Terms of the contract were not announced. The deal was first reported on Twitter by ESPN's Adam Schefter and Field Yates.
Washington, 32, is coming off a season in which he recorded 47 receptions for 658 yards and four touchdowns in 14 starts with the Houston Texans. He has also spent 10 years in the NFL with the Pittsburgh Steelers, where he was a member of the Super Bowl XL and XLIII winning teams, and Tennessee Titans.
He has 458 career receptions for 6,954 yards and 44 touchdowns in his 11 seasons.
Washington joins a wide receivers core that includes Danny Amendola, Aaron Dobson, DeAndre Carter, Julian Edelman and Chris Hogan.