Newton lost a play-off to Tom Watson at The Open in 1975 and finished joint second behind Seve Ballesteros at the 1980 Masters.
His career was ended at 33 when he lost his right arm and eye after being hit by a spinning propeller as he prepared to board a plane.
Newton went on to become a commentator and golf course designer.
In recent years he had been diagnosed with Alzheimer's disease.
"On behalf of our family, it is with great sadness I announce that our courageous and loving husband, father, brother, grandfather, and mate, Jack Newton OAM [Order of Australia] has passed away overnight due to health complications," said a statement from Newton's son, Clint.
"He fought back from tremendous adversity as only he could, and chose to selflessly invest his time, energy, and effort towards giving back to the community through his Jack Newton Junior Golf Foundation, sports commentary, golf course design, and raising significant funds for several charities, most notably, diabetes.
"His passion for sport and contributing to future generations of golfers and the Australian community demonstrates the character of our father, beloved husband, proud brother, adoring grandfather, and maverick mate."
Newton won the British Matchplay in 1974, the Buick-Goodwrench Open in 1978 and the Australian Open in 1979.
The PGA of Australia said it was "deeply saddened" by Newton's death.
It added: "His playing career and promotion of junior golf through the Jack Newton Junior Golf Foundation will ensure his legacy forever remains embedded within Australian golf."
The Sport Australia Hall of Fame said it was mourning the passing of an "esteemed member", while Golf Australia called Newton an "incredible character and golf legend".