The Bills announced in the afternoon that they had signed Edwards, but they didn't release terms of the contract.
Edwards is a six-year NFL veteran who has played his entire career with the Baltimore Ravens. He missed all of the 2008 season with a neck injury, but he bounced back last season, registering 56 tackles and two sacks in 18 games, including the playoffs.
Listed at 6-foot-3 and 290 pounds, Edwards visited Bills headquarters Tuesday. Earlier in the day, the team signed linebacker Andra Davis to a two-year deal.
The Associated Press contributed to this report.