Members of the Bills' brass spent last weekend with Kolb, and then hosted Kolb in Buffalo for a visit on Thursday and Friday.
The move gives the Bills another starting-caliber QB after they released Ryan Fitzpatrick earlier this month. Tarvaris Jackson, re-signed to a one-year contract earlier this offseason, had been the only experienced quarterback on Buffalo's roster.
Kolb was released by the Arizona Cardinals earlier this month after the sides were unable to reach an agreement on a restructured contract.
Thanks to injuries and unsteady play, Kolb appeared in just six games with the Cardinals last season, throwing for 1,169 yards with eight touchdowns and three interceptions.
Kolb, 28, threw for 17 touchdowns and 11 interceptions in two seasons with Arizona after being acquired from the Philadelphia Eagles. He was a 2007 second-round pick of the Eagles.
Information from ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.