The deal is worth $4 million, a source tells ESPN's Adam Schefter.
Mills plugged a hole for the Bills when right tackle Seantrel Henderson was diagnosed with Crohn's disease late in the 2015 season, but was a liability last season, ranking 64th among NFL tackles by Pro Football Focus.
Mills, who turned 26 in December, played his first two seasons with the Bears after Chicago drafted him in the fifth round (No. 163 overall) in the 2013 draft.
He started 29 of the 32 games he appeared in at right tackle with Chicago.
ESPN's Mike Rodak contributed to this report.