Bancroft was seen using sandpaper to try to rough up the ball in the Cape Town Test in March, receiving a nine-month ban from international and domestic cricket for his part in an incident that rocked the sport.
David Peever announced his resignation on Thursday, three days after a report saying Cricket Australia was arrogant and bent on winning at all costs in a review of its culture and governance commissioned after a ball-tampering scandal.
The International Cricket Council chief executive David Richardson says the public have made it clear that they do not want ball tampering or other forms of cheating in the sport.
Disgraced cricketer David Warner has said he accepted the 12-month ban handed down to him by Cricket Australia for his role in last month's ball-tampering scandal in South Africa.
The result ranks as Australia's second-heaviest defeat by runs, their heaviest in 90 years, and the heaviest for any team in test cricket since 1934. And that was after a ball-tampering scandal.
The usually pugnacious batsman apologised to fans, team-mates, his family and the Australian public for a ball-tampering scandal that has rocked the cricket world.
Australia's coach Darren Lehmann will step down after the fourth Test against South Africa ends. The team's captain Steve Smith returned to Australia and broke down as he took "full responsibility" for the ball-tempering plot in Cape Town.
Opening batsman Cameron Bancroft received a nine-month ban following the scandal, which has outraged fans, jolted the sponsors and prompted CA to send the trio home from South Africa.
Steve Smith, David Warner and Cameron Bancroft were involved in a ball tampering plot in the third test against South Africa on Saturday.
Australia now trails 2-1 in the series with one test to go and its proud record of having never lost a series in South Africa since 1970 is seriously under threat.
Australian cricket team captain Steve Smith said he and other senior players came up with the idea of trying to cheat and change the condition of the ball as South Africa was running away with the game.
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