Runström grew up in the southern suburbs of Stockholm and went to Enskede school as a child. He started playing football for Enskede IK at the age of six years, Runström's time in Enskede went well and at the age of 12 years he was rewarded with a move to a bigger club; Hammarby IF. Runström developed at a fast speed and when he was 16 he left Hammarby for Italy and Bologna. He stayed in Italy for three years and led Bologna to their first Italian Youth Championship in 19 years in 2001. At 17 he was part of Bologna's first team but only made the bench in Serie A and Coppa Italia. In 2002, he was transferred to Chievo Verona and after that to Florentia Viola. His stay in Florence was not what he had dreamed of and when rumours spread in late 2003 that Fiorentina wanted to trade him for the Swedish international Kim Källström of Djurgårdens IF he was outraged and declared that it was a transfer he would never accept. "Me playing for Djurgården would be like Di Canio going back to Italy to play for A. S. Roma, it won't happen, if I go back to Sweden the only club that I could think of is my old club Hammarby". Runström did return to Hammarby soon after and played three more seasons scoring 18 goals in 57 matches. This record attracted the attention of Premier League club Fulham. In July 2006, Runström joined Fulham on a three-year contract, for a fee of £700,000. After making just one Premier League appearance against Tottenham Hotspur, on 30 January 2007, Runström moved to Luton Townon loan for a month. He returned to Fulham on 1 April 2007, having scored twice for Luton, against Sheffield Wednesday and Norwich City. Later that year, in July, he was loaned out to German club 1. FC Kaiserslautern, for the 2007–08 season. On his return, in May 2008, Runström was released by Fulham. On 4 June 2008, Runström signed a three-and-a-half-year contract with Danish club OB. On 23 February 2010, Molde FK signed the Swedish forward on loan from Danish club Odense BK until the end of the season. He made his competitive debut on the opening day of the Norwegian Premier League on 14 March against the defending champions Rosenborg. He scored on his debut, a 35-yard cracker in a 2–1 loss. After this match Runström spent the rest of the season mainly on the bench, only making brief appearances not succeeding in making a mark on the matches. Runström was towards the end of the season considered redundant in Molde and the club terminated the contract with the player and sent him back to Denmark. Runström and OB parted company in February 2011. On 27 February, Runström signed for The superettan side Hammarby, On 3 July, Runström scored twice against Öster. On 28 March 2012, Runström was signed to the New England Revolution of Major League Soccer. New England declined the option of his contract on 27 June 2012 and Runström became a free agent.
