The 26-year-old defenseman, who was a restricted free agent, scored 18 points (five goals, 13 assists) and was plus-13 in 54 games last season.
Selected by the Anaheim Ducks in the second round (No. 55) of the 2014 NHL Draft, Montour has scored 91 points (24 goals, 67 assists) and is plus-20 in 243 games with the Ducks and Sabres. He has eight assists in 21 Stanley Cup Playoff games.
The Sabres acquired Montour from the Ducks on Feb. 24, 2019, for a first-round pick in the 2019 NHL Draft and defenseman Brendan Guhle.
Montour was one of six restricted free agents to receive a qualifying offer from the Sabres on Wednesday. The others were goalie Linus Ullmark, defenseman Lawrence Pilut and forwards Casey Mittelstadt, Victor Olofsson and Sam Reinhart. Ullmark, Olofsson and Reinhart filed for salary arbitration Saturday.
On Friday, Buffalo signed forward Tobias Rieder and defensemen Brandon Davidson and Matt Irwin, each to a one-year contract, and re-signed forward Zemgus Girgensons to a three-year, $6.6 million contract.