The 28-year-old forward is in the final season of a three-year, $13.75 million contract he signed July 20, 2016, with the Washington Capitals, who traded him to the Devils on July 2, 2017. He can become an unrestricted free agent July 1.
New Jersey will retain 40 percent of Johansson's remaining salary.
Johansson has 27 points (12 goals, 15 assists) in 48 games this season. He has been limited to 77 games the past two seasons with New Jersey because of injury.
"He has produced," Bruins general manager Don Sweeney said of Johansson. "He can play in different roles. He's a three-position player, as well, primarily playing more on the left side, but he has played a lot of center -- he was drafted as center."
Selected by Washington in the first round (No. 24) of the 2009 NHL Draft, Johansson has 331 points (119 goals, 212 assists) in 578 regular-season NHL games and 30 points (nine goals, 21 assists) in 72 Stanley Cup Playoff games.
The Bruins (36-17-9) are second in the Atlantic Division, three points ahead of the Toronto Maple Leafs.
The Devils (24-30-8) are 16 points behind the Carolina Hurricanes for the second wild card into the playoffs from the Eastern Conference entering their game against the Montreal Canadiens at Prudential Center on Monday (7 p.m. ET; MSG+, TSN2, RDS, NHL.TV). They traded goalie Keith Kinkaid to the Columbus Blue Jackets earlier Monday for a fifth-round pick in the 2022 NHL Draft. Defenseman Ben Lovejoy was traded to the Dallas Stars for defenseman Connor Carrick and a third-round pick in 2019 on Saturday.
"We have all seen firsthand the way Marcus has been a positive veteran influence on our young forwards," Devils general manager Ray Shero said. "He bought into our culture right away and took those players under his wing to teach them how to be pros. We wish him, his wife, Amelia, and daughter, Mila, all the best in Boston."