Nordström started his professional ice hockey career in the Swedish elite club Leksands IF in 1994. But after only one year he left Leksand IF and signed with its rivals Färjestads BK. Nordström played with Färjetad until 1998, winning the Swedish Championship in both 1997 and 1998. Then he was drafted by the Boston Bruins in the 1998 NHL Entry Draft (3rd round, 78th pick overall).