Foreign Affairs officials will soon arrive on the island of Koh Samui to offer support ahead of an autopsy on the 52-year-old, who died early Saturday, Australian time.
Warne was staying at the five-star Samujana Villas resort with four friends when they found him unresponsive in a bedroom.
One friend, Melbourne-based manager Andrew Neophitou, performed CPR for about 20 minutes in an unsuccessful attempt to revive the father-of-three.
An ambulance was then called but medicos also couldn't revive Warne before he was taken to the Thai International Hospital, where he was pronounced dead.
Thai Police say there are no suspicious circumstances surrounding Warne's death.
"No foul play was suspected at the scene based on our investigation," Thai police said in a statement.
Australian Foreign Affairs staffers have spoken to Warne's friends ahead of arriving in Koh Samui to help repatriate the body of the famous cricketer, whose family has been offered a state funeral by the Victorian government.
Premier Daniel Andrews says the southern stand at the MCG will be renamed the S.K. Warne Stand in a tribute to the legspinner who is rated among the greatest cricketers ever.
Warne's cricketing fame transcended his sport, with tributes coming from rock stars including Mick Jagger and Elton John and prime ministers and politicians of Australia, England and India.
Australia's team had just finished the opening day of play in the first Test in Pakistan when learning of Warne's death.
"Hard to fathom," Test captain Pat Cummins said.
"Warnie was an all-time great, a once-in-a-century type cricketer.
"We loved so much about Warnie. His showmanship, his charisma, his tactics, the way he just willed himself and the team around him to win games for Australia.
"The game of cricket was never the same after Shane emerged and it will never be the same now he has gone."
Warne, named as one of the five cricketers of the 20th century by the sport's almanac Wisden, is Australia's leading Test wicket-taker with 708 scalps from his 145 Tests.
In all formats, the legspinner took 1001 international wickets, earning elevation to the International Cricket Council, Australian cricket and Australian sport halls of fame.
Esteemed foes-turned-friends and Australian teammates expressed their grief at the sudden passing of Warne, who was also renowned for his larger-than-life persona and off-field exploits.
"He lived more in his life than most people would live in 20," Australia's retired fast bowler Glenn McGrath said on social media.
Ex-Australian captain Mark Taylor said Warne "had a turbulent life but a very full life ... you just felt, I certainly did, he would go on forever."
Indian legend Sachin Tendulkar was among those to post tributes on social media, saying he was "shocked, stunned & miserable".
Sir Vivian Richards said he was "shocked to the core" and his fellow West Indian Brian Lara said: "We have lost one of the greatest sportsmen of all time!"
Celebrities who befriended Warne also told of their grief.
"I'm so saddened ... he brought such joy to the game and was the greatest spin bowler ever," Mick Jagger said.
Elton John said he was heartbroken, posting: "Shane was a magical bowler and such huge fun," while pop star Ed Sheeran wrote he was "absolutely gutted" at Warne's passing.
Australia's Oscar-winning actors Russell Crowe and Hugh Jackman were among others to laud Warne as a cricketer and a mate.
