Montour, who turned 27 on Sunday, can become an unrestricted free agent after the season. The defenseman has scored 14 points (five goals, nine assists) in 38 games this season.
"Pushing the pace, creating offense, using my legs, using my energy," Montour said. "I think that's a big strength of mine. Defense first obviously, making those plays and continue up the ice and help the forwards as much as I can. In Buffalo, we struggled offensively, but hoping to get back there and get that energy going right off the bat and help these guys toward the stretch."
The Panthers are without defenseman Aaron Ekblad because of a fractured left leg. He was expected to be out 12 weeks after having surgery March 29.
"I know he's a pretty skilled defenseman," Panthers captain Aleksander Barkov said of Montour. "He can help us with the puck and offensive game. He moves the puck pretty well. Good addition and looking forward to seeing him soon."
Selected by the Anaheim Ducks in the second round (No. 55) of the 2014 NHL Draft, Montour has scored 105 points (29 goals, 76 assists) in 281 regular-season games with the Sabres and Ducks and eight assists in 21 Stanley Cup Playoff games.
"Brandon is a capable and talented right-shot defenseman who will have an immediate impact on our club," Panthers general manager Bill Zito said. "His two-way acumen and ability to play important minutes make him an exciting addition to the Panthers."
Florida (26-12-4) is third in the eight-team Discover Central Division, two points behind the Carolina Hurricanes and Tampa Bay Lightning.
Buffalo (10-25-6) is last in the eight-team MassMutual East Division.
The top four teams in each of the four divisions qualify for the playoffs.
NHL.com independent correspondent Alain Poupart contributed to this report
