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The exemption allows quarantine-free travel for the Wallabies, based on the argument that a rugby test generates up to $20 million in spending.
Today's decision means the first Bledisloe clash can take place in Auckland on August 7.
"Decisions on the other games are dependent on ongoing discussions between New Zealand Rugby and Rugby Australia," Sport Minister Grant Robertson said.
"This decision was not taken lightly by the Government and given the Wallabies use of a charter flight, there is no restriction on public access to a return flight to New Zealand," he said.
The Wallabies have already been operating in their own bubble and will travel from their base in Queensland on a charter flight to Auckland on Friday morning.
"They will have to fulfill all normal obligations for travel including negative pre-departure tests within 72 hours of their travel."
The Australian team's economic exemption for the three-test series was approved by Acting Minister for Covid-19 Response Ayesha Verrall.