The tourists will play a three-day warm up match in Fatullah from Oct. 3 before the first Test starts in Chittagong from Oct. 9. Dhaka will host the second Test from Oct. 17.
Australia won both matches the last time they played Bangladesh in 2006 and this year's series will be only the third between the two nations.
Bangladesh have made great strides in the one-day game but are still considered minnows in the longer format, ranked ninth out of 10 Test playing nations.
They reached the World Cup quarter-finals for the first time this year and since then have won ODI series at home against Pakistan, India and South Africa.
They also managed to draw a weather-hit single Test against India and are on the verge of drawing a two-Test series against world's top-ranked Test side South Africa after rain washed away a majority of the two matches.
Image: Bangladesh players celebrate after picking up a wicket
Photograph: Andrew Biraj/Reuters