Davis, a third-round pick in 2012, started the past three seasons for the New York Jets at the weakside position in their 3-4 defense and will play the same spot with the Browns, which could mean that former starter Craig Robertson, an unrestricted free agent, will not be back with Cleveland.
"There's a lot of positive energy in this building," Davis said in a statement issued by the Browns. "It seems like they're ready to take this organization in the right direction. I felt nothing but positive vibes from (executive vice president of football operations Sashi Brown) all the way down to the defensive coordinator and the head coach. ...
"I just want to be able to come in and help as best as possible. I take pride in being a run stopper. I take pride in covering. I take pride in playing in space, being a sideline-to-sideline backer. I take pride in getting after the quarterback. I just want to be able to do whatever the coach is asking of me."
The Browns also signed linebacker Justin Tuggle last week.
Last season didn't end well for Davis, who finished in a platoon with Erin Henderson. They split time over the final six games, although coach Todd Bowles insisted it wasn't because he was unhappy with Davis. He couched it by saying Henderson deserved an increased role. Nevertheless, it stung Davis, an every-down linebacker in 2013 and 2014.
Davis came from a small school, Arkansas State, but the organization placed big expectations on him. On the day he was drafted, his first coach, Rex Ryan, said Davis possessed leadership qualities that reminded him of former Baltimore Ravens great Ray Lewis -- an unfair comparison.
In four seasons, Davis has produced 332 tackles, 6.5 sacks, one interception and four fumble recoveries. He has no forced fumbles. He missed a team-high 16 tackles last season, according to Pro Football Focus. He also had problems in pass coverage.
ESPN Staff Writers Pat McManamon and Rich Cimini contributed to this report.