The Sabres fired coach Ron Rolston and general manager Darcy Regier earlier this month. Sabres owner Terry Pegula replaced Rolston with former coach Ted Nolan and also hired Pat LaFontaine as president of hockey operations during the overhaul.
"I've talked to LaFontaine a couple of times and he asked today for permission, so we gave him permission," Bruins GM Peter Chiarelli said.
Benning has been with the Bruins for eight seasons, including the last seven in his current role. Previously, he worked for the Sabres for 12 seasons, including eight as the director of amateur scouting.
"You feel proud," Chiarelli said of Buffalo's interest in Benning. "Both our assistants -- Donnie Sweeney and Jimmy -- both are very deserving of that type of thing. They've helped us and they've grown as professionals and it speaks well of the organization when that happens and you feel proud. It's always a good thing when people are advancing and this is another example of that."
The Sabres started 4-15-1, the worst start in franchise history. They've gone 1-1 since the changes.
Rolston was 19-26-6 in his brief tenure as Buffalo coach. Regier had been the Sabres' general manager since 1997.
Pegula stressed that the problems went beyond the performance of Regier, who had become the subject of "Fire Darcy" chants in Buffalo.
"He didn't do what he did by himself," Pegula said. "There was input from many people, prior owners, myself.
"Why now? I just decided, and that's the only answer I can give you. We work together, and sometimes you get to the point where a change was needed."
Information from ESPNBoston.com's Joe McDonald and The Associated Press was used in this report.