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.
Church bells in the Netherlands also played some of his biggest hits in tribute.
Bergling quit touring in 2016, two years after having both his gallbladder and appendix removed following acute pancreatitis.
"I know I am blessed to be able to travel all around the world and perform," he said at the time, "but I have too little left for the life of a real person behind the artist."
Musicians around the world remembered the star as a "genius" who was "sensitive and humble".
Calvin Harris called him "a beautiful soul, passionate and extremely talented with so much more to do"; while Diplo described him as "the gold standard" and "the best of this generation".
Fellow dance artist Marshmello said "At a loss for words. Rest easy brother."
"Nobody can deny what he has accomplished and done for modern dance music," added Deadmau5.
Fans have been revisiting Avicii's music in the wake of his death, with three of his singles set to return to the UK chart this week.
The 2013 song Wake Me Up, which is one of the UK's best-selling singles of all time, is at number 13 in the midweek chart update; while Avicii's breakthrough hit Levels is at 24, followed by Hey Brother at 32 (current rules will only permit a maximum of three songs to re-enter the singles chart).
Avicii's two studio albums True and Stories are also set to return to the Top 40, while his remix album True - Avicii by Avicii is at 23.