Authorities believe the journalist died aboard an inventor's homemade submarine.
"The DNA of the torso matches that of Kim Wall," Copenhagen police announced on Twitter.
In a grisly case that has gripped public imagination, Danish inventor Peter Madsen has been accused of the negligent manslaughter of 30-year-old Kim Wall as she interviewed him aboard his 60-foot (18-metre) submarine on August 10.
She had been missing since then.
The female torso, with the head and limbs deliberately cut off, was found on Monday in Koge Bay, around 50 kilometres (30 miles) south of Copenhagen.
Copenhagen homicide chief Jens Moller Jensen told a news conference there were injuries to the torso which appeared to suggest that air had been forced out of it.
He also said the torso had been attached to a metal object which was likely intended to weigh it down.
Police are still searching for the remaining body parts.
The cause of death was still unknown, Jensen added.
”I would like to express my deepest sympathy with Kim Wall’s family [to] whom we had to give the definitive news last night that we now have a DNA match between Kim Wall and the torso found,” he said.
”Naturally, the DNA match is a relatively large break through in the investigation which will now continue until we have built all possible information in the case.”
Swedish journalist Kim Wall was onboard a private submarine 'UC3 Nautilus' owned by Peter Madsen. The submarine sank on 11 August. Source: AAP
Blood in the submarine
Police also said they had found her blood inside the submarine.
"We secured a hairbrush and a toothbrush to confirm her DNA. We found blood in the submarine and it was a match," Jensen said.
Wall, a freelance journalist who had reported for The Guardian and The New York Times, has not been seen since boarding Madsen's submarine on August 10.
She had met with Madsen to interview him for a feature story she was writing.
Madsen, 46, and Wall were seen on board the vessel by several people in waters off Copenhagen the evening of August 10.
Photos of the two emerged online standing next to each other in the sub's tower. Wearing an orange fleece and with her long auburn hair tied in a topknot, she appeared to be smiling.
Her boyfriend reported her missing a day later. The same day, Madsen was rescued from waters between Denmark and Sweden shortly before his submarine sank.
Madsen, whose website describes him as an "inventepreneur", initially told authorities he dropped Wall off on an island late on the evening of August 10.
But he changed his story several days later when he appeared in court, saying Wall had died in an accident on board and that he dumped the body at sea at an undefined location in Koge Bay.
'Endless sorrow'
Police have since said they believe Madsen, 46, "deliberately" sank the sub. It was brought to the surface and searched, but found to be empty.
Madsen has been in custody since August 12 suspected of negligent manslaughter, but Jensen said Wednesday the formal charge could change following the latest developments. He will remain in custody until September 5.
A graduate of Columbia School of Journalism, Wall was based between New York and China.
Her friends have described her as "invincible", "ambitious" and as "seeing something good in everyone", according to Swedish media reports.
"It is with endless sorrow and dismay that we have received the news that the remains of our daughter and sister have been found," Wall's mother Ingrid wrote in a Facebook post on Wednesday.
Wall had covered news about earthquake-hit areas in Haiti, Idi Amin's torture chambers in Uganda and minefields in Sri Lanka.
"She gave voice to the weak, to the vulnerable and marginalised people," her mother wrote.
"That voice would have been needed much, much longer. But now that will not be so."
