Published: 2020-03-11 21:53:20 BdST
The first Test will be played from June 11 in Chattogram while the second Test will be played from June 19 in Dhaka, with 120 points up for grabs in the World Test Championship.
Australia are second in the Championship standings with 296 points, behind leaders India, while Bangladesh have yet to open their account.
The last time Australia toured Bangladesh, the series ended 1-1.
After the Bangladesh series, Australia visit Scotland for a one-off Twenty20 at the end of June before visiting England for three T20 matches and three one-day internationals in July.