The governing body announced Peever’s departure in the wake of the independent review into Australian Cricket following the ball-tampering scandal on the tour of South Africa in March.
Earl Eddings has taken over as interim chair and said in a statement: “We thank David for his service.
“He has played a pivotal role in the elevation of women’s cricket, and the significant growth in attendance and participation.
“He should also be acknowledged for his efforts in improving funding to the ICC full member nations outside Australia, England and India; overhauling governance of the ICC and reforming the Future Tours programme, among a long list of achievements.
“We look forward to continuing the important process of recovering and rebuilding for Cricket Australia and Australian Cricket.
“The board is keenly aware that we have a way to go to earn back the trust of the cricket community. We and the executive team are determined to make cricket stronger.”
After the publication of the 145-page review, which said the governing body had to take its share of the blame for a “win-at-all-costs” culture, Peever admitted it had been a “difficult and confronting time for everyone involved”.
But Peever said he was “not embarrassed at all” and expressed his desire to oversee cultural changes outlined in the review’s 42 recommendations.
Peever, who joined the Cricket Australia board in 2012 and became the chairman three years later, is the latest casualty of the ball-tampering scandal.
Australia captain Steve Smith and deputy David Warner were given one-year bans and Cameron Bancroft, who carried out the cheating in South Africa, received a nine-month suspension.
Coach Darren Lehmann, unaware of the ball-tampering plan, resigned and has since revealed he is having counselling to deal with the scandal, while long-serving chief executive James Sutherland retired.