Rolston, 47, replaced Lundy Ruff, who was fired in February after leading the Sabres for more than 14 seasons.
Buffalo went 15-11-5 in 31 games under Rolston but missed the playoffs, finishing 12th in the Eastern Conference. He previously coached two seasons at Rochester of the American Hockey League, building a 63-44-17 record.
Rolston, the older brother of recently retired NHL player Brian Rolston, also spent seven seasons as head coach with USA Hockey's national team development program. He became the first coach in U.S. history to lead the team to three gold medals at the Under-18 IIHF world championship.