Greig was 66. He breathed his last at a hospital here after being brought in a "critical condition".
He was diagnosed with lung cancer in October this year after undergoing treatment for what was initially thought to be bronchitis in May.
He underwent tests after the World Twenty20 Championships in Sri Lanka and it was revealed that there was a small lesion at the base of his right lung.
"On his return to Australia he had fluid removed from the right lung and testing revealed he had lung cancer," the 'Sydney Morning Herald' reported.
Greig's son Mark told a newspaper that his father's cancer had progressed to "stage four".
While commentating during the coverage of the first Australia-South Africa in November, Greig spoke about the disease.
"It's not good. The truth is I've got lung cancer. Now it's a case of what they can do," Greig had said. MORE
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