While the dates of the tour are yet to be announced, it is likely to be in mid-September.
India last played a Test against Australia in 2006.
The pink ball Test between India and Australia will be only the second such match to be held in the history of women's cricket.
The only day-night women's game played so far was between Australia and England at Sydney in November 2017. The match ended in a draw.
Preparing for both the England and Australia Test will be a challenge since the women don't play with red ball even on the domestic circuit.
"It will be a challenge for sure but the good thing is that women are getting to play Tests," a former India player said.
"The pink ball game in Australia will be a tougher challenge as the girls have never played with that ball but I am sure they will get to prepare well for it. A few practice games will also be needed," she added.
England and Australia are the only two teams which regularly play Test cricket, mainly against each other in the Women's Ashes.
Going forward, India will also be seen playing the longest format against the two teams.
"As players, we've said for a long time that we'd love to play more Test matches," Australia captain Meg Lanning said on Wednesday.
"It's an exciting prospect and I know (India) are heading over to England to play a Test match pretty soon so it shows they're up for the challenge and really willing to play that format."
India's Tour of Australia Full Schedule:
~ Sept 19: First ODI, North Sydney Oval (D/N)
~ Sep 22: Second ODI, Junction Oval
~ Sep 24: Third ODI, Junction Oval
~ Sep 30 – Oct 3: Day/Night Test match, WACA Ground (D/N)
~ Oct 7: First T20, North Sydney Oval
~ Oct 9: Second T20, North Sydney Oval
~ Oct 11: Third T20, North Sydney Oval.