As announced by Australian prime minister, Scott Morrison earlier

The travel bubble will first open up to vaccinated students and business travelers before moving on to tourists soon after, with Morrison saying that Australia is in the "final stages" of concluding an agreement with Singapore on the matter. Adding that:

We anticipate that being able to be achieved within the next week or so, as we would open up to more visa class holders coming out of Singapore, we will see that occur.

But the arrangement will also be dependent on whether Australian states ease their quarantine measures that have been in place for all international travelers.

So far, New South Wales and Victoria have already planned to scrap hotel quarantine from 1 November with the former stating that Australian citizens and permanent residents will be allowed to resume international travel from 1 November as well.