The selling price is reportedly around $1.4 billion. The rest of the league's owners must approve the deal, which would likely happen at the next scheduled owners' meeting Oct. 7-8 in New York.
On Monday, at least three ownership groups reportedly submitted bids to buy the Bills, including the Pegulas, a group led by real estate mogul Donald Trump and another group that included rock star Jon Bon Jovi. The Pegulas were reportedly the front runners due to their local ties and commitment to keeping the Bills in Buffalo.
The team was put up for sale after owner Ralph Wilson died in March.
Terry Pegula, who made his fortune largely through natural gas development, has owned the Sabres since February 2011. In the three seasons since Pegula took over, the team's winning percentage has declined each year, with the team finishing with the lowest points total in the Eastern Conference in 2013-14.
Pegula also owns the Rochester Americans of the American Hockey League and the Buffalo Bandits of the National Lacrosse League. In 2011, he donated $100 million to alma mater Penn State to help fund the creation of men's and women's varsity hockey programs as well as a new ice arena named for him.
NFL commissioner Roger Goodell said earlier this year that the Bills, which Forbes values at $935 million, need a new stadium to remain viable in Western New York.
The Pegulas are worth a reported $3.5 billion.
- Scooby Axson, Ben Estes and Chris Johnson