Björling, 19, was found dead at his home in Gotland last week. The cause of his death has not been made public.
The news was only made public in a statement released by the teenager's family on Wednesday.
"My beautiful loved fantastic son Tristan has left us," his father wrote on Facebook.
Björling had impressed judges in the early stages of the competition but was eliminated in September's qualifying week.
The news has stunned the producers of the TV4 show, which regularly pulls in ratings of more than a million viewers per episode.
"I'm shocked and incredibly sad, it's so terribly tragic when such a talented person leaves us. Tristan had a talent that affected the whole of Sweden and he will live on in our hearts," said Swedish musician and Idol judge Anders Bagge in a statement.
To honour the young singer a minute's silence has been held at his school in Visby. He was due to perform at the opening of a new youth centre on the day that his death was announced.
TV4 have said they are offering support and counselling for the remaining contestants in this year's Idol following the news of Björling's death.
"We feel deeply for Tristan's relatives. They have expressed the wish to be left alone in their grief and we will do all that we can to support them," Pelle Porseryd, executive producer of Idol, said in a TV4 statement.
Sweden's Idol series is now in its tenth season.