The team announced the news on its Twitter account early Monday.
The extension does not come as a surprise. General manager Tim Murray indicated on several occasions that the two sides were close to completing a deal.
Nolan returned for a second stint in Buffalo in mid-November, when he was hired on an interim basis. He took over for Ron Rolston, who was fired along with GM Darcy Regier, after Buffalo got off to a franchise-worst 4-15-1 start.
The Sabres (20-45-9) remain in last place, and in the process of rebuilding from scratch.
[Stamkos] is a great teammate and a great leader, that's why he's got the 'C'. He brings that tremendous work ethic to the rink and he's one of the top players in the game. I know if I put the passes where they are supposed to be, there's a very good chance he's going to put it in the back of the net.
— Lightning forward Jonathan Drouin on linemate Steven Samkos
TONIGHT ON NHL NETWORK
5:00 ET: NHL Live Powered by Constellation 7:00 ET: NHL Tonight Western Conf. Preview 8:00 ET: 2015 Blackhawks Championship Film