Danish authorities have been searching for Wall, a 30-year-old reporter who had been writing a feature story about Madsen, since she failed to return from an interview with him aboard the 60-foot (18-metre) Nautilus.
In a statement, police said Madsen - who has been accused of negligent manslaughter - had told them and the court that there was an accident on board the sub that led to the death of Kim Wall, and that he subsequently buried her at sea in an undefined location of the Koge Bay, south of Copenhagen.
The pair were sighted on board the vessel by several people in waters off Copenhagen the evening of August 10.
The sub was also reported missing, but rescue crews located it around midday on August 11 in Koge Bay, about 50 kilometres (30 miles) south of the Danish capital.
Just after being found, Madsen was rescued and the submarine suddenly sank.
The Nautilus was the biggest private sub ever made when Madsen built it in 2008.
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