Initially, Madsen said he had dropped her off in Copenhagen but later changed his story to say she died in an accident after hitting her head on a hatch and he had "buried her at sea".
Police in Denmark said Saturday they discovered the head and legs of missing Swedish journalist Kim Wall in waters near Copenhagen.
Police have previously said they were re-examining the unresolved case of a Japanese tourist whose mutilated body was found in a Copenhagen harbour in 1986, to see if there was any possible link to the Wall case.
The cause of death of the journalist is not yet established.
The pathologist has now also identified Kim Wall with the help of her teeth.
During their investigation, police have found videos on Madsen's personal computer of women being tortured, decapitated and murdered.
Almost two months after the death of Kim Wall, the Danish police announced that it had made a new discovery macabre.
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The 18-meter UC3 Nautilus was recovered by the Danish military with only Madsen aboard, while Wall was nowhere to be found.
The independent writer disappeared in the wake of boarding a secretly assembled submarine with its Danish innovator, Peter Madsen, on August 10. The charge sheet alleges Madsen cut Wall's body into pieces, punctured her torso and tied pipes to it to make it sink to the bottom of the sea.
Madsen has insisted there was no sexual relationship between him and Wall, and that their contacts had been professional.
He said the police would continue to search for her arms.
Her torso had also been weighed down when it was found, also in Koge Bay.
Read the full New York Times article. Madsen was rescued from the sinking vessel and brought ashore, where he was picked up by police, but there was no trace of the missing journalist.