Brown, 28, has played on one-year contracts each of the past two seasons. He was named to the Pro Bowl in 2016, when he had 97 solo tackles, 4.0 sacks and one interception while starting all 16 games for the Buffalo Bills.
Last season with the Redskins, he started all 13 games in which he played and collected 84 solo tackles and 2.5 sacks.
Brown was one of four Redskins linebackers eligible for free agency this year. Trent Murphy reportedly signed with the Buffalo Bills, while Will Compton and Junior Galette remain unsigned.