The 28-year-old was found dead on Friday in Oman's capital city, Muscat. A cause of death has not been released.
"Two post mortems were carried out," Royal Oman Police said, confirming there was "no criminal suspicion".
Avicii, whose real name was Tim Bergling, had been in Oman on holiday. His family have arrived in the country to return his body to Sweden.
Thousands of fans gathered in central Stockholm over the weekend to honour the musician, who scored huge worldwide hits with Wake Me Up and Levels.