The deal was reached before a scheduled arbitration hearing Friday in Toronto.
The 25-year-old Swede was one of the top free agents when he signed with the Stars two years ago. He had 17 goals in 55 games as a rookie but struggled with a shoulder injury last season. He had two goals in 44 games.
Brunnstrom starred in the Swedish Elite League before choosing Dallas over the Detroit Red Wings and other NHL suitors.