The 2019 Rugby World Cup will be held in Japan while the 2023 event bid was controversially won by France last month after voters ignored a World Rugby evaluation report that said South Africa had the strongest bid.
Australia were the sole hosts of the tournament in 2003 and co-hosts with New Zealand in the inaugural World Cup in 1987.
The nation has never hosted the women's World Cup. The eighth version was held in Ireland earlier this year, where Australia finished sixth.
"The Rugby World Cup is the pinnacle for our Wallabies and Wallaroos teams and we want to bring those tournaments home for any player, boy or girl, man or woman, who ever dreamed of lifting the Cup here on our home soil," Rugby Australia chairman Cameron Clyne said in a statement.