"DNA match between torso and Kim Wall," the police said on Twitter, declining to comment further until a later press briefing.
Danish inventor Peter Madsen, charged with killing Wall on his home-made submarine, told the court she had died in an accident and that he "buried" her at sea, changing his previous statement that he dropped her off alive in Copenhagen.
The body was found on Monday by a passing cyclist and police said then it was too early to identify the body which was missing its head, legs and arms.
The case has been followed closely by Danish and Swedish media and has drawn interest from around the world.
Madsen has been charged with manslaughter of Wall who has been missing since he took her out to sea in his 17-metre submarine on August 10. He denies the charge.
He was rescued a day after his UC3 Nautilus sank. Police found nobody else on the vessel.
Danish and Swedish maritime authorities used divers, sonar and helicopters in the search for the body in Koge Bay, south of the city, and in the Oresund Strait between the two countries.
Madsen, an entrepreneur, artist, submarine builder and aerospace engineer, appeared before a judge on August 12 for preliminary questioning. The case is not open to the public to protect further investigations, police said.
