Hester, 46, had failed to return home after taking his two dogs for a walk on Friday night. The drummer's body was later found in a park near his home in the southern city of Melbourne.
Ambulance officers arrived on the scene shortly after midday Saturday and tried to resuscitate him, but "he was dead when they arrived," Metropolitan Ambulance Service spokeswoman Liraje Memishi said.
Memishi said he had "attempted suicide" and then suffered strangulation. She declined to confirm where Hester's body was found. Reports have said he was discovered hanging from a tree.
Hester played in several small bands before joining the New Zealand group Split Enz in 1983. He and Split Enz singer Neil Finn formed Crowded House in 1985 with bass player Nick Seymour.
Crowded House was one of Australia's most successful bands in the late 1980s and early 1990s, with international hits such as "Don't Dream it's Over" and "Weather with You."
Peter Green, a longtime friend of Hester, reportedly contacted Finn and Seymour after learning of the drummer's death.
Green said Hester had experienced "some dark moments," but dismissed media reports that he was struggling with depression or illness at the time of his death.
"Paul never said anything about that and I never, ever, heard he was suffering from any illness," he told The Daily Telegraph newspaper for its Monday edition. "Then, after today, I wonder if anybody really knew anything."
Seymour also expressed surprise at the news, telling the paper he seen Hester in Ireland two weeks ago.
"It was all good," Seymour told the paper from Dublin. "The last words Paul told me were: 'I love you, mate. See you in town (Melbourne) in a month'."
Finn, currently touring in London, said he was deeply saddened at the loss of his friend.
"I am devastated," he told the paper. "I have lost one of my best mates."
Hester quit Crowded House in 1994, citing the pressures of touring and declining motivation for the group.
He is survived by his girlfriend Mardi Sommerfield and their two daughters aged 8 and 10.