Pro Football Focus rated Brown as the NFL's 42nd-best linebacker in 2017.
He tweeted a farewell to Buffalo on Friday.
Thank you to everyone in Buffalo and all of Western New York for an amazing four years! Buffalo will always have a special place in my heart. I will always have a tremendous amount of love and respect for not only the amazing fans, but also my teammates and coaches. Thank you! pic.twitter.com/A1RV9jHUjn— Preston Brown (@PB_Number2) March 16, 2018
The Bengals didn't have much room left in their available salary-cap projections after re-signing tight end Tyler Eifert and trading for Bills left tackle Cordy Glenn, but Brown fits the mold they've been targeting in free-agent linebackers the last few years. Karlos Dansby and Kevin Minter also signed for one-year deals. It didn't appear the Bengals would re-sign Minter after injuries limited him to only nine games last season, leaving them with a hole at middle linebacker.
The Bengals favor players with durability, and Brown, a Cincinnati native, has shown versatility by playing both inside and outside linebacker in a 4-3 scheme as well as inside linebacker in a 3-4 scheme.
Brown, 25, has not missed a game since being selected by the Bills in the third round of the 2014 draft, starting 62 of the 64 games in which he has played.
He has played at least 98 percent of defensive snaps for the Bills in each of the past three seasons, and 93 percent in 2014. He has worn the Bills' radio helmet to receive play calls from three different defensive coordinators since his rookie season.
ESPN's Katherine Terrell contributed to this report.