Skilled migrants and international students, as well as Japan and South Korean citizens, will be among those allowed entry from 1 December.
All must be fully vaccinated.
Australia has implemented some of the world's tightest border controls since March last year, including on its own citizens.
Prime Minister Scott Morrison called Monday's announcement an "important step forward".
Under the relaxed rules, eligible visa holders will be allowed to return to Australia without needing a special exemption.
