The Bills had been shopping Edwards before his release, a league source told ESPN NFL Insider Adam Schefter.
Edwards was named the starting quarterback to start the season after winning a competition in training camp but was benched after Week 2 in favor of Ryan Fitzpatrick.
Brian Brohm is the other quarterback on the Bills' roster.
Fitzpatrick was 20 of 28 against the New England Patriots on Sunday with two touchdowns and two interceptions in the Bills' 38-30 loss.
Edwards was in his fourth season in Buffalo after being selected by the team in the third round of the 2007 draft out of Stanford. He went 14-18 as a starter, including 0-2 this season.
He was benched a day following a 34-7 loss at Green Bay on Sept. 19 after going 11 of 18 for 102 yards and two interceptions.
In two games, Edwards went a combined 29 of 42 for 241 yards passing with a touchdown and two interceptions. He was sacked seven times.
The Bills' have made five in-season changes at quarterback in six years. The team hasn't had a regular starter since Drew Bledsoe's three-year tenure ended in 2003.
Adam Schefter is ESPN's NFL Insider. Information from The Associated Press was used in this report.
