ESPN.com's Adam Schefter reports that the deal is worth $45 million, with $20 million guaranteed.
Hughes, 26, has spent the last two seasons with the Bills. In 2014, he had a career-high 53 tackles, with 9.5 sacks and three forced fumbles, helping lead the league's fourth-ranked defense.
NFL teams were allowed to begin negotiating with free agents this weekend. Contracts cannot be signed until 4 p.m. ET on Tuesday.
Last week, the Bills acquired running back LeSean McCoy in a trade with the Philadelphia Eagles for linebacker Kiko Alonso. McCoy reportedly signed a new five-year, $40 million contract with the Bills with $26.5 million guaranteed.
- Mike Fiammetta and Scooby Axson