The Bruins also added checking line forward Curtis Lazar, who has missed the past six games with an upper body injury. Buffalo acquired fourth-year forward Anders Bjork and a second-round pick in a deal completed before the NHL's trade deadline.
The blockbuster deal was initially reported by Sportsnet's Elliotte Friedman.
As part of the deal, the Sabres agreed to retain half he remainder of Hall's one-year, $8 million salary. The NHL's 2018 MVP was deemed expendable by last-place Buffalo, which is already retooling for beyond this season.
"I still believe in myself as a player. I still feel like I can add things to a team. ... That's what makes me really excited," Hall said. "I really just want to be part of a winning team. However I can do that, I'm all-in."
The Bruins have lost two straight following an 8-1 loss to the Washington Capitals on Sunday. At 21-12-6, they hold the East Division's fourth and final playoff spot, and are four points ahead of the New York Rangers and Philadelphia Flyers.
Boston has four players on injured reserve, including forward Ondrej Kase and defenceman Brandon Carlo. In the meantime, defencemen Charlie McAvoy missed his fourth game with an upper body injury, and defenceman Matt Grzelcyk is also sidelined.
In a separate trade on Sunday, the Bruins also acquired defenceman Mike Reilly from the Ottawa Senators for a third-round pick.
The Sabres, by comparison, are in sell-off mode with the team all but assured of matching the NHL playoff drought record of 10 seasons. Buffalo traded defenceman Brandon Montour to Florida on Saturday, and previously traded veteran centre Eric Staal to Montreal.
The Sabres began sitting out Hall for precautionary reasons since Tuesday in anticipation of a trade.
Hall was the key to the deal because he was considered one of the few remaining impact forwards still on the market. Questions, however, have been raised as to whether his drop in production is the result of the 29-year-old having lost a step or because he's playing on a struggling Sabres team that is 29th in goals-per-game.
Hall, the No. 1 pick in the 2010 draft, was limited to two goals and 17 assists for 19 points in 37 games, and is in the midst of a 16-game goal drought. That's a considerable drop from his 2017-18 MVP season in New Jersey, where he posted career-bests with 39 goals and 93 points in 76 games.
"It was such a whirlwind of a year. It went pretty badly, obviously," Hall said. "It wasn't the season I would have like to have, not even close. These last few days you do some soul-searching, look to what you could do better in the future."
Hall is on to his fourth team in two years. He was traded by New Jersey to Arizona last season, and then became a free agent after negotiations broke down with the Coyotes because of internal turmoil, which led Bill Armstrong taking over as general manager.
Buffalo acquired the 24-year-old Bjork, who had two goals and three assists in 30 games this season, a year after generating a career-best nine goals and 19 points in 58 games. Overall, the 2014 fifth-round draft pick out of Notre Dame has 16 goals and 39 points in 138 career games with Boston.
Little has gone right for Buffalo. Coach Ralph Krueger was fired on March 17, and the Sabres' season was undone by mounting injuries and a pause for two weeks following a COVID-19 outbreak in early February.
Hall was among the most sought forwards on the free agent market in October, and surprised many by signing with Buffalo. He was reunited with Krueger, who played a key role in mentoring Hall during his first three seasons in Edmonton.
Krueger pushed for the signing, making the case to management that Buffalo was one player away from being a contender despite coming off a season in which the team finished 13th in the Eastern Conference and one spot from qualifying for the expanded playoffs.
Hall was initially interested in staying in Buffalo upon signing with the team. His focus began changing by eventually acknowledging he was open to waiving his no-trade clause last month while the team was in the midst of an 18-game winless skid -- the NHL's 14th longest.