The appeals court judgment means that the case will not be reheard at Stockholm District Court.
"We have reached the conclusion that we do not agree with the conflict of interest claim," appeals court judge Anders Eka told news agency TT.
Norström is a member of several organizations that take a pro-copyright stance. These memberships formed the basis of accusations from defence lawyers that the judge was biased and led to calls for a retrial.
Defence lawyers pointed out in appealing the convictions of their clients - Peter Sunde, Fredrik Neij, Carl Lundström and Gottfrid Svartholm Warg - on charges of complicity in breach of the Copyright Act, that one of the organizations receives funding from the recording industry organization IFPI.
The Court of Appeal conceded that the judge was a member of organisations acting in the interests of rights holders, but the court also pointed out that copyright holders enjoy constitutional protection under Swedish law.
"For a judge to back the principles on which this legilsation rests cannot be considered bias," the court wrote in its ruling.
The court did however criticize Norström for not speaking openly about the organizations of which he was a member prior to the start of the trial. This would have allowed for the bias claims to be heard at an earlier stage of the legal process, the court said.
But while the judge was negligent in his duty to inform the court of such details, this was not sufficient reason for the district court verdict to be declared null and void, according to the three appeals court representatives behind Thursday's ruling.
Tomas Norström declined to comment on the appeals court ruling.
But newly elected member of the European Parliament Christian Engström of the Pirate Party was outraged and surprised by the court's decision.
"This is part of a pattern. It show that the Swedish legal system is no longer to be trusted when it comes to copyright cases. It's a travesty of justice quite simply," Engström told TT.
"There are certainly problems with the laws too but this also shows that the courts are not capable of applying the laws in a correct manner. I've been a lay judge for seven years and I've never seen an indictment as bad as the Pirate Bay verdict. But that didn't stop the court from setting ridiculous sentences," said Engström.
Membership of the Pirate Party skyrocketed after Stockholm District Court on April 17th sentenced four of the men involved with the Pirate Bay to a year in jail. And Engström believed that Thursday's ruling would have a similar effect.
"This makes it clear that the only way to win this battle is through politics. It's a political issue and it's going to be decided at the general election in 2010," he said.