He is playing his first tournament since suffering serious injuries in a car accident in December 2022 that kept him out of last year's IPL as well as the 50-overs World Cup in India
The tour will follow Australia's white-ball tour of West Indies in July.
Australia had initially pencilled in three matches but a Cricket Australia spokesman said on Wednesday it was their intention to play five.
Dates and venues are yet to be confirmed.
Australia were set to tour Bangladesh last year for two tests before it was postponed due to the COVID-19 pandemic.
The T20 World Cup is slated for October but the tournament may be moved if India is unable to overcome a devastating second wave of the novel coronavirus.