In initial police questioning, Madsen, who is suspected of her death, had denied cutting up her body and said she died in an accident when a heavy submarine hatch fell on her head.
He has now changed his story to say she died of carbon monoxide poisoning while on board, police said in a statement.
“He has now explained that Kim Wall died as a result of carbon monoxide poisoning inside the submarine at a time when he was on deck,” police said.
“Furthermore, Peter Madsen has admitted that he later dismembered her corpse and spread the body parts in Koge Bay” off Copenhagen.
Wall, a freelancer based in China and New York, never returned from her interview with Madsen on August 10.
Her headless torso was found floating in Koge Bay on August 21, and her head, legs and clothes were recovered in plastic bags in the same waters on October 7.
Madsen, a self-taught engineer and inventor, has been held in custody since August 11 and has changed his version of events several times.
After intentionally sinking his submarine early on August 11 in Koge Bay, he was picked up by a rescue vessel and told police he had dropped Wall off on land after their interview the previous evening.
On September 5, he changed his story to say a 70-kilo (154-pound) hatch fell on her head, killing her, and that he threw her body overboard, intact, in a panic.
But police said on October 7 that an autopsy of her head showed no sign of a skull injury.