Anders Eklund, 42, has also confessed to killing 31-year-old Pernilla Hellgren in Falun in central Sweden in 2000.
Eklund is not currently suspected of any further crimes but a spokesman for the National Criminal Investigation Department said they were comparing his crimes to previously unsolved cases.
“We’re looking at all relevant unsolved murders and missing person cases,” Paul Johansson told news agency TT.
Police said they would conduct a detailed examination of Eklund’s movements both at work and in his private life.
“We’ll also look at how the crimes we find were committed. We’ll compare the perpetrator’s behaviour with the crimes we know he has committed,” said Johansson.