At the age of 18, Cuthbert won three gold medals at the 1956 Melbourne Olympics - the 100m, 200m and 4x100m relays.
Known as Australia's "golden girl", she went on to win gold in the 400m at the Tokyo Olympics eight years later.
She passed away in Western Australia on Sunday night after a long battle with multiple sclerosis.
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Australian Prime Minister Malcolm Turnbull led tributes on social media calling the runner an "inspiration and a champion on and off the track".
Friend and former Olympic sprinter Raelene Boyle said Cuthbert had won medals with "humility and distinction".
"A lot of the athletes today could take a great deal of learning out of the way she did it," Boyle told the Australian Broadcasting Corp.
Cuthbert, who was diagnosed with multiple sclerosis in 1969, was a torchbearer at the Sydney Olympic Opening Ceremony in 2000.
"Athletics Australia is saddened to confirm the passing of Olympic legend Betty Cuthbert, our thoughts with her family and friends," Athletics Australia announced on Twitter.
Cuthbert, who set nine world records during her career, was the first Australian to win triple gold.

A four-mile section of the A591 between Keswick and Grasmere remains closed after it was damaged in a landslide.
Cumbria County Council said it had upgraded a forest road at Dunmail Raise which is wide enough for a small bus but not general traffic.
A spokesman said the service would begin on Tuesday.
A spokesman said there would be a park and ride service with pick up points at Keswick, Legburthwaite and Grasmere.
Australian sprinting legend and four-time Olympic gold medallist Betty Cuthbert has died aged 79.
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A shuttle bus service is being put in place to help passengers stranded after the collapse of a major road during Storm Desmond.