The veteran received a one-year contract worth around $5 million including incentives, sources told Ian Rapoport of NFL Network.
The Bengals released Burfict on Monday, ending his tenure with the club after seven seasons. The former Pro Bowler registered 33 tackles over seven games in 2018.
"We're on the same team," Burfict said of Brown to Michael Gehlken of the Las Vegas Review-Journal after inking his deal. "It's one goal. It's all positive, man. He's a great player. ... I'm going to approach him just like I do all my other teammates. ... There's nothing negative here. We're on the same team. We're trying to win a championship here."
Burfict's history of distasteful plays is extensive, and he's frequently drawn fines from the league as a result.
He's also endured a troubling history of concussions, picking up the seventh documented head injury of his NFL career last year.