Brunnström began playing professionally in Sweden's third highest hockey league with Jonstorps IF from 2005 to 2006, scoring 44 points in 38 games.

Negotiations with Brunnström came to a head towards the end of the season, with the Detroit Red Wings, Montreal Canadiens, Toronto Maple Leafs and Vancouver Canucks widely considered to be the initial front-runners in landing him.

[4][5] After completing the season with 37 points in 54 games, Brunnström eventually signed with the Dallas Stars on 8 May 2008 to a two-year entry-level contract.

Making the Red Wings' 2011–12 starting roster, on 3 October 2011, Detroit signed Brunnström to a one-year two-way contract which assured him $105,000 in AHL and $600,000 at the NHL level.

[11] After a year’s hiatus, Brunnström returned to the professional circuit for one last season in 2016–17, playing with Rungsted Seier Capital in the Danish Metal Ligaen.