Ole Christian Bach, 48, was wanted by Interpol in 182 countries and had been on the run since last autumn.
Swedish police had apparently received word that Bach was in the Stockholm area and investigators spotted him outside a grocery store on the island of Ekerö. According to the police's account, Bach drove off and officers in two unmarked cars gave chase.
After driving a short way, Bach pulled over. When police approached his car they found him dead with a pistol beside him. He had shot himself in the head.
"In stressful situations he always carried a gun," said Bach's lawyer, Håkon Schiong.
"He was terrified of hit men," he told Expressen.
Schiong said he suspected that Bach thought he was being chased by "people from the underworld" rather than police.
But some doubt has been cast on the police's version of events, after the Norwegian news agency NTB spoke to witnesses who reported seeing a high-speed chase in which the police cars collided with Bach's car.
This was confirmed by Norwegian police and the dead man's car, a Saab 9-5 hired from a Statoil petrol station in Stockholm, was said to have been damaged down one side. There was further confusion on Tuesday morning when press conference apparently called by the Swedish police failed to take place.
Bach's lawyer has called for an investigation into the events surrounding his death, while his fiancée told the Norwegian media that he had just popped out to get lunch and that it was "unthinkable" that he would have killed himself.
According to Expressen, Ole Christian Bach "swindled financiers, porn kings and housewives". In 1988 he was sentenced to four years in prison for his role in a pyramid scam worth hundreds of millions of kronor. A few years later he was found guilty of receiving Edvard Munch's Madonna, which was stolen from an Oslo gallery.
Norway's economic crimes unit launched an investigation against Bach, who was one of the country's richest men, in October 2004. Expressen illustrated the risks he took by describing a recent visit to Oslo.
"He parked his car in the garage directly under [the economic crimes unit] headquarters and then went and had lunch with his lawyer in the district court's restaurant across the street."
"He lived an insanely dramatic life and had an equally dramatic death," said Bach's lawyer.