The conditional second-round pick becomes a first-round selection in the 2013 NHL Draft if Boston advances to the Eastern Conference Finals in this year's playoffs.
Jagr, 41, has picked up 14 goals and 12 assists for 26 points in 34 games with the Stars this season.
The two-time Stanley Cup champion is in his 19th NHL season, having played in 1,380 career NHL regular-season games to date, and has picked up 679 goals and 1,000 assists for 1,679 points with the Pittsburgh Penguins, Washington Capitals, New York Rangers, Philadelphia Flyers and Stars.
The Flyers, Montreal Canadiens and Detroit Red Wings were also interested in acquiring Jagr.
MacDermid, 23, was originally drafted by the Bruins in the fourth-round (112th overall) of the 2009 NHL Entry Draft.
He played in three games with the Bruins this season, registering 10 penalty minutes.
Payne, 19, was selected in the fifth-round (145th overall) by the Bruins in the 2012 NHL Draft.