Terms of the deal were not disclosed.
Last season, Meriweather started all 13 games in which he appeared for Washington and was credited with 93 tackles while also recording two interceptions, one sack, one forced fumble and one fumble recovery.
Meriweather was originally selected by the New England Patriots with the 24th overall pick of the 2007 NFL Draft. In seven NFL seasons, the two-time Pro Bowl choice has appeared in 89 career regular-season games with 58 starts for the Patriots (2007-10), Chicago Bears (2011) and Redskins (2012-13).
For his career, Meriweather has posted 349 tackles and 15 interceptions, one of which he returned for touchdown, to go along with five forced fumbles, three sacks and two fumbles recovered.