It will be the first Test series between the two countries since 2017, while Bangladesh have not played the longest format Down Under since 2003.
The opening game of the series in Darwin will start on 13 August followed by the second Test in Mackay from 22 August.
The series is part of the World Test Championship (WTC) and will start a run of 20 games in the format for Australia between August 2026 and July 2027.
Cricket Australia chief executive Todd Greenberg said: "It is no secret the international calendar is now crowded and we're fortunate to have world class facilities available in August ensuring we have another window for Test cricket outside summer."
Following the series at home against Bangladesh, Australia will tour South Africa for three Test matches before the home summer which includes a white-ball tour by England then the New Zealand Tests.
The Aussies then have a big five-match Test series in India during January and February before hosting England at the MCG in March for the 150th anniversary Test.