Melbourne-born Geyer, one of Australia's most respected and successful soul singers, was discovered to have inoperable lung cancer while being treated in hospital.
She died surrounded by family and friends, her record label Mushroom Records announced on Tuesday.
"Naturally, we are all utterly devastated," a statement said.
"Just last month, Renee sang to a full house and was looking forward to another busy year ahead doing what she loved most.
"She lived her life as she performed - to the fullest - and her passing leaves a giant void in the Australian music industry."
Geyer fronted a number of bands in the 1970s, including jazz-rock group Sun, before beginning her four-decade solo career.
In 1973, the first of her 15 studio albums was released.
But it was her 1974 cover of the James Brown classic It's a Man's Man's Man's World that launched her to a mass audience.
The singer was inducted into the ARIA Hall of Fame in 2005 and became the first woman to be inducted into the Music Victoria Hall of Fame in 2013.
She also received the inaugural Lifetime Achievement Award at the Australian Women in Music Awards in 2018 and appeared on the ABC's music quiz show Spicks and Specks.
Mushroom Group chief executive, Matt Gudinski, who is the son of legendary promoter Michael Gudinski, said Geyer was a "fierce, independent, strong and passionate" trailblazer for women in the music industry.
"Renee always did things her own way and we loved her for that," Mr Gudinski said.
Geyer continued to perform and release music after she was diagnosed with breast cancer in 2009, with her last album released in 2013.
She was spared a criminal conviction in 2017 over an abusive and intimidating racist rant in 2015 that caused a Sydney hotel receptionist to cry and fear for her safety.
It wasn't her only time fronting court, twice avoiding convictions for careless driving after two car crashes in Melbourne.
A 2013 poll ranked her the seventh-best Australian voice of all time.
Fellow soul singer and friend Kate Ceberano said Geyer carved the word woman into the psyche of the Australian music mentality.
"You strutted into our hearts and lives with your soul in your sleeve," she wrote on Facebook.
"Renee the powerful, the diva, the brutal, the original, the temperamental, the stellar, the shapeshifter, the original, the unforgettable, the irreplaceable Renee!"
Australian music legend Marcia Hines described Geyer as a game changer, a soul diva, her sister in song and possessing one of the greatest voices she has ever heard.
Joe Camilleri of The Black Sorrows described Geyer as a "singer's singer."
"Let's not forget the many who were influenced by Renée. Her contribution should never be forgotten.Soul free in sweet harmony," Camilleri posted on Facebook.
Geyer sang backup vocals on a number of Hoodoo Gurus albums, prompting the band to post on social media she had changed all their lives for the better.
"Renee was a fiercely original talent who carved out a huge legacy in Australian music," the band posted.
A memorial for Geyer will be held at a later date.
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