Boston general manager Peter Chiarelli announced the deal after his team's 4-3 loss at home to Toronto. The Bruins are tied with Montreal atop the Northeast Division.
"It was important to get this one done. We need help in a couple of areas and this is one of the areas," said Chiarelli, a former assistant GM with the Senators who knows Kelly well from his days in Ottawa.
The Bruins learned last week that they will play the rest of the season without center Marc Savard, who was placed on long-term injured reserve Monday with his second concussion in less than a year.
Boston sends Ottawa its second-round pick in this year's draft in exchange for the 30-year-old Kelly, who had 12 goals and 11 assists this season for the last-place Senators.
"He's a smart player and a responsible player," Chiarelli said. "He can play up the middle and he can play the wing, but he's a natural center."
Kelly is under contract through the end of next season. In 462 career games, he has 75 goals and 101 assists.
"It's pretty tough to get traded. It's my first time, but these things happen, especially the way things have gone this year," Kelly said. "I get an opportunity to play in the postseason and an opportunity to go, hopefully, deep in the playoffs."
He won't have to wait long to return to Scotiabank Place. Ottawa hosts the Bruins on Friday night.
"It'll be a weird feeling coming out on the other side of the rink. Ottawa's all I know, being drafted here and playing my whole career here," Kelly said. "I would have loved to have been part of the organization for a long time to come, but that's not the case and I wish them a lot of luck going forward."
Chiarelli said the Bruins, who were one win from reaching the Eastern Conference finals last spring, are still in the market for another defenseman and hope to make another deal before the trade deadline Feb. 28.
The rebuilding Senators traded fan favorite Mike Fisher to Nashville last week for the Predators' first-round pick in this year's draft.
"I just traded one of the good guys and most-respected players on this hockey team," Senators general manager Bryan Murray said after Ottawa's 4-3 shootout loss to the New York Islanders. "To have to make the moves we're making are difficult, but that's the way we have to go at this point in time."