Davis' deal is worth $4.4 million maximum for the two years, with $2 million coming in the first year, a league source told ESPN NFL Insider Adam Schefter.
The deal was reached during Davis' visit to the Bills headquarters, five days after the player was released by the Denver Broncos.
"Very excited. I'm glad this process is over with," said Davis, who will be a candidate to start at one of two middle linebacker spots in Buffalo's new 3-4 defense. "I feel good, man, just ready to go."
Listed at 6-foot-1 and 250 pounds, Davis is an eight-year NFL veteran who was credited with 90 tackles in each of his past two seasons. He also had a career-best 3½ sacks last year.
Rather than questioning why he was released by the Broncos, Davis prefers looking ahead.
"I know I did my best in Denver and can look myself in the mirror knowing that," Davis said. "I know I have a lot left in my tank."
He spent his first seven seasons with Cleveland, the last six as a starter after the Browns selected him in the fifth round of the 2002 draft out of Florida. Davis has 12 sacks in 96 starts and appeared in 121 career games
In Buffalo, Davis is reunited with new Bills defensive coordinator George Edwards, who served as the Browns' linebackers coach in 2004.
Davis credited Edwards' presence as a key reason he signed with the Bills.
"He was a huge factor. Not only do I know him, but he knows me and the type of player I am," Davis said.
Davis becomes the second significant player the Bills have signed since the NFL's free-agency period opened on March 5. He has the potential to fill a key need on a defense will rely heavily on its linebacking corps under the new scheme being installed by first-year head coach Chan Gailey.
His signing is also considered insurance if Aaron Schobel elects to retire this offseason. Schobel, a defensive end who could play linebacker, has not made up his mind on whether to return for a 10th season.
The Bills also reached agreement with free-agent defensive end Dwan Edwards. His four-year contract, signed Wednesday, is worth $18 million, a league source told Schefter.
Edwards, a six-year NFL veteran who played his entire career with Baltimore, was considered one of the top free-agent defensive linemen and expected to command millions per season. Multiple teams pursued Edwards -- Seattle and Denver among them -- but teams had reservations about the neck injury that prevented him from playing in 2008.
He bounced back last year, registering 56 tackles and two sacks in 18 games, including playoffs.
Listed at 6-foot-3 and 290 pounds, Edwards visited the Bills' headquarters Tuesday.
Information from The Associated Press was used in this report.