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"In sad news, beloved Tony Greig, former England Cricket Captain has passed away today at the age of 66. To his family and friends we pass on our best wishes," broadcaster Channel Nine, which employed Greig as a cricket commentator, said on Twitter.
Greig, who played 58 tests for England, was diagnosed with lung cancer in October.
The South Africa-born Greig made his test debut for England against Australia in Manchester in 1972 and amassed 3,599 runs for an average of 40.43 until his last match at the Oval against the same opponents in 1977.
An imposing figure standing at 6ft-6in, Greig was also a successful bowler with 141 test wickets at an average of 32.20.
Greig's captaincy ended in controversy when he was stripped of the post for his role in helping late Australian businessman Kerry Packer set up World Series Cricket in the 1970s.
Greig, a long-time resident Down Under, became a summer fixture in Australian lounge-rooms as a commentator for Channel Nine's international cricket coverage, among a number of roles in the media.