The two teams were scheduled to play one-day internationals in Hobart on January 12, Sydney on January 14 and finally Perth on January 17.
However, with Cricket South Africa set to host a new domestic Twenty20 competition, the governing body wanted to make their international stars available for the inaugural season.
The three-match series against Australia was past of the ICC Super League which ultimately determines qualification for the 2023 Men's World Cup.
Due to South Africa's withdrawal, Australia have been automatically handed competition points.
Cricket Australia chief executive Nick Hockley said: "It is disappointing that Cricket South Africa will be unable to contest the ODI series in January.
"That said, we are delighted to be hosting South Africa for the three Test series which includes the Boxing Day and New Year's Tests and with the comprehensive schedule of international cricket that will take place across Australia throughout the summer.
"This will include the ICC Men's T20 World Cup and a record six touring teams for the Men's and Women's international series as well as the twelfth season of the BBL and the eighth season of the WBBL."
Cricket South Africa boss Pholetsi Moseki added: "CSA is always keen on honouring its bilateral commitments. While CSA is committed to honouring its fixtures in respect of the Future Tours Programme there will sometimes be unforeseen circumstances that would negate this resolve.
"In the case of the Australia tour, CSA reached out to its counterpart months ago to reschedule the tour to mutually aggregable dates. CSA offered four options to that effect. Unfortunately, and to our disappointment, none of these were acceptable to Cricket Australia.
"CSA has agreed that ICC award Australia the competition points. While we are saddened at losing the crucial points, we are confident that our in-form Proteas team will garner the requisite points through the remaining games to secure automatic qualification to the showpiece event in India next year.
"As difficult as this decision has been for CSA, the long-term sustainability of our new T20 League is reliant on having all our domestic players available for this exciting new addition to the CSA calendar."