Brown, who finished with a team-leading 127 tackles last season, will receive a three-year, $24 million contract, NFL Network reported.
Brown, 28, used his speed to help make an impact in his only season with the Redskins' defense, giving them something they lacked. He was leading the NFL in tackles through 13 games before having to miss the final three because of a knee issue.
Brown, who battled various leg injuries for much of the season, was most productive playing behind a healthy Jonathan Allen and next to Mason Foster. Brown also finished with 2.5 sacks and was named as a Pro Bowl alternate.
He had signed a one-year deal with Washington after a productive season with the Buffalo Bills in 2016, when he was second in the NFL with 149 tackles and was a Pro Bowl selection in addition to earning second-team All-Pro honors.
Brown spent his first four seasons with the Tennessee Titans, who drafted him in the second round in 2012.