The Bills later confirmed the deal, which ESPN reported is for $2 million with $1 million in incentives.
Young, who backed up Michael Vick last season for the Philadelphia Eagles, worked out for the Bills last week and threw to four receivers, including David Nelson, who said the six-year veteran "looked good."
"We think adding Vince to our roster will create more competition for the backup quarterback position," Bills general manager Buddy Nix said in the team's announcement of the deal. "He brings with him some unique physical abilities that most are aware of and that will make the competition interesting. It's all about improving our team."
Young went on Twitter to discuss his new team.
Thanks to Buddy Nix and Coach Gailey for giving me the opportunity to come in and play and compete.
- Vince Young (@VinceYoung) May 11, 2012
Young also tweeted: "I am looking forward to playing with the guys and helping where I am needed. I have always respected the Bills organization and am looking forward to being a part of the team."
Young will compete for the backup quarterback spot with Tyler Thigpen behind starter Ryan Fitzpatrick.
Young wasn't re-signed by the Eagles after completing his one-year contract. He started three games for Philadelphia last season, throwing for 866 yards and four touchdowns with nine interceptions.
He also spent five years with the Tennessee Titans, who selected him No. 3 overall in the 2006 NFL Draft.
Young has thrown for 8,964 yards and 46 touchdowns and rushed for 1,459 yards and 12 scores during his NFL career.