Paul Hester, 46, had last been seen alive on Friday night, when he left his home with his dogs.
Ambulance officers said he had "attempted suicide" and died from strangulation. He was already dead when they arrived at the scene.
Hester played with New Zealand group Split Enz before forming Crowded House with Neil Finn in 1985.
Police have said the death was not suspicious.
Peter Green, a long-time friend of Hester, said he had not been aware of any sign of depression.
"Paul never said anything about that and I never, ever heard he was suffering from any illness," he said.
"Then, after today, I wonder if anybody really knew anything."
Hester had become a TV presenter after leaving the band in 1994.
He lived in Melbourne with his partner and daughters aged 8 and 10.
International hits by Crowded House included Don't Dream It's Over and Weather With You.