The Associated Press first reported that the two sides had come to an agreement pending compensation.
Bylsma, 44, reportedly met with the Sabres on Wednesday and Thursday, with reports suggesting a deal was "imminent."
Bylsma was fired by the Penguins after the 2013-14 season. His contract runs through next season, but he had permission to interview with other teams. In six seasons as a head coach, all in Pittsburgh, Bylsma amassed a record of 252-117-32.
Bylsma coached the Penguins to the 2009 Stanley Cup after replacing Michel Therrien as interim coach toward the end of the season. He won the Jack Adams award in 2011, and Pittsburgh made the playoffs in all six of his seasons on the bench.
Bylsma replaces Ted Nolan, who was fired in April, at the helm in Buffalo.
- Jeremy Woo