Burton, 24, was a fifth-round pick of the Vikings in 2011. He played in 11 games his rookie season, but appeared in just four contests last season. He was waived by the Vikings on Saturday.
The Bills had a need at the position, with top cornerback Stephon Gilmore out six-to-eight weeks with a fractured wrist.
Their roster currently stands at 51 players, with two open spots.