News broke in the early hours of Saturday that the 52-year-old had died of a suspected heart attack in Koh Samui, Thailand.
Reuters news agency is reporting one of Warne's friends performed CPR on him after finding the 52-year-old unresponsive in a villa.
Warne was taken to the Thai International Hospital but could not be revived.
Warne, who was born in the Melbourne suburb of Upper Ferntree Gully, leaves behind daughters Brooke, 24, and Summer, 20, and son Jackson, 22.
His family has been offered a state funeral by the Victorian and Commonwealth governments.
Victorian Premier Daniel Andrews also announced the MCG's Great Southern Stand would be renamed the S.K. Warne Stand.
Mr Andrews said the stand would be a "permanent tribute to an amazing Victorian".
"Nobody who saw Shane Warne play will ever forget him," Mr Andrews said. "To us, he was the greatest – but to his family, he was so much more.
"Our hearts are breaking for Shane's family and friends."
Foreign Affairs Minister Marise Payne said Department of Foreign Affairs and Trade officials have spoken to those travelling with Warne, and will arrive in Koh Samui on Saturday.
"DFAT is working with Thai authorities to confirm arrangements following his passing, assist with his repatriation and provide other assistance on the ground," she said.
Prime Minister Scott Morrison offered his condolences to the Warne family in a written statement.
"Shane was his own man, following his own path," Mr Morrison said.
"In those times when he could have been knocked down by the headlines, he got back up. He always did.
"We have lost one of Australia's greatest cricketers and today we are bewildered by this sad and sudden loss."
Federal Treasurer and fellow Victorian Josh Frydenberg described the former star as a "unique character with a remarkable talent".
"For Australians he was family," Mr Frydenberg tweeted. "We watched him. Laughed with him. Admired him.
"Will miss you, mate. Rest In Peace."
Federal Opposition Leader Anthony Albanese said Warne was one of the greatest cricketers the game has known.
"It was a joy to watch him play," Mr Albanese tweeted. "My thoughts go to the ones who loved him the most. We will miss you Warnie."
Deputy Prime Minister Barnaby Joyce said Warne was a "genius" and the 52-year-old's death was an incredible shock.
Hollywood star Russell Crowe tweeted he was having a hard time accepting the news.
"Genius player. Grand company. Loyal friend," he tweeted.
Rolling Stones frontman Mick Jagger said he was saddened by Warne's passing.
"He brought such joy to the game and was the greatest spin bowler ever," he tweeted.
British Prime Minister Boris Johnson described Warne as "one of the nicest guys you could meet", noting his work with disadvantaged children.
Former Australian prime minister Kevin Rudd said the cricketing legend was "larger than life".
"A living legend. No longer with us. Far too young," Mr Rudd tweeted. "Both cricket and the country so much poorer for his passing."
Australian actor Magda Szubanski, who worked with Warne on the sitcom Kath & Kim, said she was in utter shock.
"Inconceivable that a life crammed with so much genius and larrikin charm could be snuffed out so suddenly and so soon," she posted on Instagram.
"This is a shocking loss for our nation and for the cricketing world. And poor Sharon has lost her hero and the love of her life."
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