The singer’s record label, the Mushroom Group, confirmed the sad news, adding she was in no pain and died peacefully with family and friends.
“Renée is one of the most highly regarded singers in contemporary music – her unique vocal sound influences countless singers to this day,” a statement read.
The label said it was discovered Geyer also had inoperable lung cancer while she was in hospital.
“We are all utterly devastated,” a spokesperson said.
Geyer most recently performed to a sellout crowd last month and the record label said the singer had been looking forward to a busy year ahead.
“Renée was irrepressible, cheeky and loyal and her musical legacy speaks for itself, with her performing and recording career spanning five decades,” the statement said.
“(She) lived her life as she performed – on her own terms and to the fullest.
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“Beloved and respected, she was a force of nature and a national treasure, and her passing leaves a giant void in the Australian music industry.”
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The Melbourne-born artist was inducted into the ARIA Hall of Fame in 2005 and was the first woman to be inducted into the Music Victoria Hall of Fame in 2013.
She has also received the inaugural Lifetime Achievement Award at the Australian Women in Music Awards in 2018.
“We would like to thank the staff at the University Hospital Geelong for their care and consideration,” the record label said.
Details of Geyer’s memorial are yet to be announced.