The Bills also announced Monday that they signed cornerback Corey White and receiver Leonard Hankerson, who finished last season in Buffalo. Brown and White signed shortly after meeting with Bills officials at the team's headquarters.
Brown spent four seasons with the Tennessee Titans, who selected him in the second round of the 2012 draft. His career was derailed after he tore a pectoral muscle in Tennessee's 2014 season opener.
He came into the league as an outside linebacker and was shifted inside when the Titans moved to a 3-4 front in 2014.
In 2015, Avery Williamson became an every-down linebacker, and Wesley Woodyard played better as a starter in his second season with the Titans, leaving Brown as a situational player. He had just five starts in 16 games last season.
Before being shifted inside in 2014, the 26-year-old Brown had 9.5 sacks in his first two seasons. He also has six interceptions, two coming in 2015.
White split last season between Arizona and Dallas after spending his first three in New Orleans. He has four interceptions in 51 career games, including 20 starts.
Hankerson spent his first four seasons with Washington, and has 107 catches for 1,408 yards and nine touchdowns.
ESPN Titans reporter Paul Kuharsky and The Associated Press contributed to this report.