"We have been informed today that Tjostolv Moland is dead. He was found in his prison cell in Kinshasa this morning," Foreign Minister Espen Barth Eide told reporters.
When asked about the cause of death, he replied only that Norway had "no comment at this time."
Moland and his friend Joshua French, who has dual British-Norwegian nationality, were sentenced to death for murder and spying in the vast central African country in 2010.
Shortly after their conviction Moland, 32, and French, 31, wrote to Congolese President Joseph Kabila to ask for a pardon or for their death sentence to be commuted to life imprisonment that could eventually be served in Norway.
Norwegian authorities have since been trying to negotiate a transfer to the Scandinavian country.
Former soldiers French and Moland, who claimed they were in the country to set up their own security company, were first sentenced to death in 2009, convicted of having killed the driver of the car they had rented in May that year. They insisted the driver was killed by bandits.
The verdict was annulled for irregularities by the high military court in 2010, but a new panel of judges convicted them in a retrial in June that year of spying, criminal association, murder and attempted murder.
A prison official claimed in August 2011 that the pair — who met in the Norwegian army — had tried to escape from prison, but their lawyer denied this.
DR Congo has not carried out a death sentence since Kabila came to power in 2001, but has commuted such penalties to life imprisonment.
Barth Eide said a Norwegian diplomat has been sent to the Kinshasa prison following the news of Moland's death.