There was a "DNA match between [the] torso and Kim Wall", Copenhagen police said early on Wednesday.
Ms Wall was last seen alive on 10 August as she departed on a submarine trip with inventor Peter Madsen.
The submarine sank hours after the search for Ms Wall began. Mr Madsen was charged with negligent manslaughter.
He initially said he had dropped her off safely near Copenhagen, but has since said she died in an accident and that he had "buried" her at sea.
Danish police believe the 40-tonne submarine was deliberately sunk by Mr Madsen. He denies any wrongdoing.
Lead investigator Jens Moller Jensen said that DNA had been taken from Kim Wall's hairbrush and toothbrush and it matched the remains found on a beach south of Copenhagen on Monday.
The torso was mutilated in an apparent attempt to ensure that decomposition gases passed out of the body, and there was also metal attached to it to make it sink, he added.
Blood found on the submarine itself had also been identified as belonging to the Swedish journalist. He would not comment on the cause of death but said a post mortem examination was being carried out and police were still looking for the rest of her body.
- Who is DIY submariner Peter Madsen?
What we know
"During the horrendous days since Kim disappeared, we have received countless examples of how loved and appreciated she was, as a person and as a friend, as well as a professional journalist," Ingrid Wall said in a family statement released on Facebook.
"From all corners of the world we have received testimony to how she was able to be a person who made a difference."
What happened to Kim Wall?
Ms Wall, 30, was reported missing by her boyfriend in the early hours of 11 August, after she failed to return from a trip on Peter Madsen's homemade submarine, the Nautilus.
A freelance journalist who had written for the Guardian, New York Times and South China Morning Post, she was researching a feature about the inventor and the Nautilus, which he built in 2008 with crowdfunding.
Emergency services scoured the area of sea to the east of Copenhagen and the submarine was eventually spotted from a lighthouse south of the Oresund bridge between Denmark and Sweden. Within 30 minutes the vessel had sunk and Mr Madsen was rescued.
Police said the next day that the arms, legs and head had been deliberately cut off. They finally confirmed it was Kim Wall in a tweet early on Wednesday.
Mr Madsen's lawyer, Betina Hald Engmark, says her client has not confessed to anything. He pleaded not guilty in a closed-door judicial hearing earlier this month.
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