Reilly has 19 assists in 40 games this season for Ottawa and has scored 72 points (eight goals, 64 assists) in 244 games for the Senators, Canadiens and Minnesota Wild.
"Obviously I played in Montreal for a bit and being able to play in Boston and when Boston came to the Bell Centre, obviously it was some spirited games, for sure," Reilly said. "I love the way Boston plays and I also know a couple guys on the team that have already reached out to me. So definitely excited to get going here."
Reilly signed with the Wild as a free agent July 3, 2015, after his junior season at the University of Minnesota. He was selected by the Columbus Blue Jackets in the fourth round (No. 98) of the 2011 NHL Draft but did not sign with them.
The Bruins (21-12-6) are in fourth place in the eight-team MassMutual East Division, four points ahead of the New York Rangers and Philadelphia Flyers. The Senators (13-25-4) are in last in the seven-team Scotia North Division. The top four teams in each of the four divisions will make the Stanley Cup Playoffs.
Boston was without four defensemen, Charlie McAvoy, Matt Grzelcyk, Kevan Miller and Brandon Carlo, in an 8-1 loss to the Washington Capitals on Sunday. Though Miller was held out as a maintenance day after he missed all of last season to multiple knee surgeries and is expected to return Tuesday against the Buffalo Sabres, return dates remain unknown for the other three, each out with an upper-body injury.
Grzelcyk was injured in a 3-2 loss at the Philadelphia Flyers on Saturday and is considered day to day. McAvoy, who last played April 5, skated Sunday and could be available Tuesday. Carlo, who is out with an injury that is unrelated to the concussion that cost him 10 games from March 7-28, has missed the past six games and is week to week.
The Bruins also acquired forwards Taylor Hall and Curtis Lazar from the Sabres on Monday for forward Anders Bjork and a second-round pick in the 2021 NHL Draft.
Hall signed a one-year, $8 million contract with the Sabres on Oct. 11 and can become an unrestricted free agent after this season. The 29-year-old forward has scored 19 points (two goals, 17 assists) in 37 games this season.
Lazar, who can become an unrestricted agent after the season, has not played since March 31 because of a lower-body injury. The 26-year-old scored nine points (five goals, four assists) in 33 games for Buffalo this season.
NHL.com staff writer Amalie Benjamin and independent correspondent Matt Kalman contributed to this report