Terms of the deal were not disclosed by the Redskins, but multiple media outlets reported that it was a three-year, $24 million contract.
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 a team-best 84 solo tackles and 2.5 sacks.
Brown spent his first four seasons with the Tennessee Titans, who drafted him in the second round in 2012.
For his career, Brown has totaled 537 tackles along with 19 passes defensed, 16.5 sacks, seven interceptions, four fumbles forced, three fumbles recovered and two touchdowns.
Brown is the second inside linebacker to be re-signed by Washington this offseason, joining Mason Foster.