Jones signed a one-year deal with the Bills on Friday, Alec White & Maddy Glab of the team's official site reports.
Jones finished the regular season with 35 tackles (22 solo), including one sack, and one interception on six passes defended in 13 games.
Jones logged seven total tackles (four solo), including one tackle for loss and 1.0 sack in Sunday's 26-0 loss to the Jaguars.
Jones (coach's decision) is inactive Sunday against the Vikings.
Jones was signed to the Panthers' active roster Wednesday, Darin Gantt of the team's official website reports.
Jones signed a one-year contract with Carolina on Monday, Adam Schefter of ESPN reports.
Jones recorded seven tackles (four solo), two passes defensed and an interception in Sunday's 23-10 loss to the Bengals.
Browns coach Kevin Stefanski said that Jones is a likely candidate to take over as the team's starting middle linebacker after Sione Takitaki suffered a season-ending torn ACL on Sunday, Scott Petrak of the Elyria Chronicle-Telegram reports.
Jones finished Sunday's loss to Miami with nine tackles (three solo), including a half-sack.
Jones is set to become the Browns' starting middle linebacker, Anthony Poisal of the team's official site reports.