The 30-year-old, who had been due a $3m (around £2m) bonus today and $10m (£6.68m) in salary in 2013, started all 16 games for the Bills last season.
Fitzpatrick told WGR-AM: "This isn't something that all of a sudden was thrown at me, I was blindsided by it, this is something that we talked about for a week or two.
"It stinks. I really did enjoy being a Buffalo Bill, and unfortunately we couldn't get anything worked out."
General manager Buddy Nix said in a statement: "Our focus remains on adding another quarterback to our roster and we will continue to explore every option available to us."
Fitzpatrick spent four seasons with the side, having previously played for the Cincinnati Bengals and St Louis Rams.