Moore has signed a five-year deal with the Bruins at an average annual value of $2.75 million, TSN.ca reports.
Moore's 20:28 of ice time in Tuesday's 6-2 loss to the Sharks was second on his team, but he accrued just one shot and one block.
Moore tied for the team lead with four shots, but he failed to get on the scoresheet in Thursday's 3-2 loss to Calgary.
Moore saw his two-game point streak come to a close after being held off the scoresheet in 19:31 of ice time during Tuesday's 4-1 win over the Islanders.
Moore is set to play in his 400th career game Thursday night against the visiting Rangers.
Moore scored the overtime winner in Monday's 4-3 triumph at Minnesota.
Moore recorded a team-high 25:34 of ice time in Friday's 5-4 shootout win over the Senators.
Moore scored an overtime goal and picked up an assist in Thursday's 5-4 win over Ottawa.
Moore scored his 10th goal of the year in overtime Tuesday -- the only tally in a 1-0 win over the Flyers.
Moore scored both of the Devils' goals -- one on the power play -- in Thursday's 4-2 loss to the Leafs.