Dennison spent the past two seasons as the Denver Broncos' offensive coordinator, helping the team win the Super Bowl after the 2015 season. This was his second stint in Denver after he spent 15 seasons with the organization from 1995 to 2009.
The 58-year-old also spent four years as the Houston Texans' offensive coordinator.
He will now run the offense for newly hired head coach Sean McDermott, who has experience on the defensive side of the ball.
Dennison's offense struggled this past season, finishing 22nd in the NFL in points scored and 27th in total yards. Those struggles contributed to a disappointing 9-7 season one year after Denver won the title.
However, the coach's vast experience as a coordinator, plus as an offensive line coach and quarterbacks coach, should help him succeed in his new position.
Interestingly, his long coaching career on the offensive end has come after he spent nine years as a linebacker with the Broncos.
The Bills are looking for a fresh start after their 7-9 season under former head coach Rex Ryan in 2016.
Buffalo had surprisingly already hired much of its offensive staff, including offensive line coach Juan Castillo and tight ends coach Rob Boras. Both coaches have been coordinators in their careers, but the organization waited to make a final decision on its new offensive coordinator.
For a franchise that hasn't reached the playoffs since 1999, the team is hoping these moves can make the difference.