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.