Norrena started his pro hockey career with TPS in the SM-liiga, winning four Finnish championships. In 2003 he won the Swedish Championships with Frölunda HC before joining Linköpings HC in the Swedish Elitserien. He has represented Finland numerous times in international play, including as number-two goaltender in the 2006 Winter Olympics and as number-one goaltender in the 2006 World Championships.

 

On May 31, 2006, the Tampa Bay Lightning announced they have signed Norrena to a one-year entry level contract. However, on June 30, he was traded to the Columbus Blue Jackets along with Fredrik Modin for Marc Denis. Norrena made his NHL debut on October 14, 2006, against the Minnesota Wild, stepping in to replace Pascal Leclaire in the second period. Norrena eventually took over as number-one goaltender for Blue Jackets for the 2006-07 season, playing 55 out of 82 games in his first NHL-season. Norrena also made a team record, keeping his goal clean for 155 minutes and 28 seconds in a row. Blue Jackets re-signed Norrena in February 2007 with a two-year contract. He is now serving as the backup to Columbus' number one goaltender, Pascal Leclaire.