At a press conference, chief investigator Jens Møller Jensen said police had linked the victim to the torso with DNA obtained from her toothbrush and hairbrush. Blood found on the submarine was also a match for Wall, he said.
Møller Jensen said the body had apparently been punctured to let the air out before sinking it, and it was weighted down in a presumed attempt to prevent it floating.
Wall, 30, had boarded a 17-meter, privately built submarine on August 10 for a story she was writing about its inventor, Peter Madsen.
She was last seen on that day in an image that allegedly showed her standing with Madsen in the tower of the submarine in Copenhagen Harbor.
A passing cyclist found the torso Monday afternoon on the southwest side of Amager island near the Danish capital.
Police had earlier said the body appeared to have been deliberately dismembered.
"Naturally, the DNA match is a relatively large breakthrough in the investigation which will now continue until we have built all possible information in the case," said Møller Jensen.
Investigators and divers are carrying out an extensive search Wednesday for "remaining body parts and clothing" in coastal areas of Amager island, he said.
In a statement posted to Facebook, Wall's mother, Ingrid Wall, spoke of the family's "immense grief and shock" on learning that the journalist's remains had been found, and said many questions remained unanswered.
She recalled the impact of her daughter's disappearance on her family, friends and colleagues around the world, as well as the powerful stories she had told from remote corners of the planet.
"Following Kim's disappearance, we have received countless messages about how loved and appreciated she was -- as a human being, as a friend and as a journalist. It's a true testament to the impact she's had on others," she said.
"She gave a voice to weak, vulnerable and marginalized people. It's a voice this world needed for years to come, but that has now been silenced."
An ongoing mystery
Madsen, who has been charged with manslaughter, told a closed-door court hearing Monday that Wall had died in an accident and was buried at sea in an "unspecified place" in Køge Bay, according to a statement.
Madsen, 46, originally claimed he had dropped her off on land on the night of August 10, according to a police statement.
But police later said Madsen had provided them with a "different explanation."
The inventor was charged with manslaughter on August 11 and ordered to be held in custody for 24 days.
His lawyer Betina Hald Engmark told Denmark's TV2 at the time that her client "accepts the arrest but still denies the crime."
According to CNN's Swedish affiliate Expressen, the submarine -- which had sunk -- was found at 10:30 a.m. on Friday, August 11, 15 hours after it had departed Copenhagen.
Police said there was no trace of Wall when the submarine was found by emergency services.
Expressen reporter Federico Moreno, speaking to CNN from Amager island near where the torso was found, said the search effort appeared to have intensified since Tuesday.
He said he could see about 10 divers searching the waters off the island, more than double the number he'd seen a day earlier. The spot where the torso was found is also not far from the location where the submarine sank, he said.
Danes with whom Moreno has spoken about the case say the circumstances are very strange and that they have questions about Madsen's changing accounts of what happened, he said.
Moreno said that Madsen's lawyer, Hald Engmark, had sent him a text message after Wednesday's police press briefing to say that Madsen maintained his innocence.
Madsen was already famous in Denmark before his name hit the headlines in relation to this case, Moreno said. He had launched his submarine, the UC3 Nautilus, in 2008 with the help of crowdfunding.
Wall wasn't a household name in Sweden, in part because she mostly wrote for English-language publications, Moreno said, but she was an experienced reporter and her family is well known in media circles.
Wall, a graduate of Columbia University and London School of Economics, was based between Beijing and New York. Her work appeared in the New York Times, the Guardian and TIME among others.
Her father was a photojournalist for Expressen for many years and her brother also works as a photojournalist for Swedish publications, Moreno said.