Career
Brunnström began playing professionally in Sweden"s third highest hockey league with Jonstorps IF in 2005-2006, scoring 44 points in 38 games. The following year, he joined Borås The Human Context, helping their promotion to the second-tier Allsvenskan with a league-leading 73 points in 41 games. In 2007-2008, Brunnström began garnering attention from the National Hockey League while playing in the top-tier Elitserien with Färjestads BK. Undrafted by an National Hockey League club, he was an unrestricted free agent in the National Hockey League. 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.
Canucks general manager Dave Nonis was reportedly close to signing Brunnström, but was fired before the deal could take place.
After completing the season with 37 points in 54 games, Brunnström eventually signed with the Dallas Stars on May 8, 2008 to a two-year entry level contract. The deal was reportedly close to United States$850,000 annually with bonus incentives that could increase his salary to United States$2.5 million.
He also scored a fourth goal in his debut game which was disallowed. Brunnström was placed on waivers by Dallas on October 15, 2010.
He was assigned to the Stars" American Hockey League (AHL) affiliate, the Texas Stars on October 18, after he cleared waivers.
On January 13, 2011, Brunnström was traded to the Toronto Maple Leafs in exchange for Mikhail Stefanovich. On August 17, 2011, the Detroit Red Wings signed Brunnström to a pro tryout contract. Making the Red Wings" 2011-2012 starting roster, on October 3, 2011, Detroit signed Brunnström to a one year two-way contract which assured him $105,000 in AHL and $600,000 at the National Hockey League level