The electronic dance music star, real name Tim Bergling, was found dead in Muscat, Oman, on Friday afternoon.
He was twice nominated for a Grammy Award and was responsible for hits including Wake Me Up and Levels.
However in recent years he battled health problems, which forced him to retire from touring in 2016.
He suffered from acute pancreatitis and had his gallbladder and appendix removed in 2014.
On Saturday, thousands of people gathered at Sergels torg – the most central public square in Stockholm, the city where Avicii was born – to pay tribute.
His publicist confirmed the death on Friday with "profound sorrow".
"The family is devastated and we ask everyone to please respect their need for privacy in this difficult time," he said.
His death came days after he was nominated for a Billboard Music Award for top dance/electronic album.
Avicii tweeted his thanks for the nomination on Tuesday, just days before his death.
Musician Nile Rodgers, DJ Calvin Harris and singer Rita Ora were among those to pay tribute.
Rogers, a friend and collaborator posted a message on Twitter about the DJ, who he described as his "little bro".
He said: "I was just told my dear friend Tim @avicii just passed away. Please let this be a hoax. If not £RIPAVICII one of the best natural melody.
"Dear Tim your family have my most heartfelt condolences. You were my little bro. Love always.
"I'm crying on the airplane. I hope I don't make the passengers nervous."
Scottish DJ Harris was another to share a tribute message, calling his fellow musician a "beautiful soul".
He tweeted: "Devastating news about Avicii, a beautiful soul, passionate and extremely talented with so much more to do. My heart goes out to his family. God bless you Tim x."
Ora, who collaborated with Avicii on his final track, Lonely Together, wrote on Twitter: "I have no words. I remember how amazing it was to make Lonely Together and it felt like just yesterday we were talking.
"Condolences to Avicii's family, friends, and the fans who supported him. May he rest in peace. Gone too soon. I'm devastated. Heartbroken."
