Canberra offered the settlement in June after 1,905 men alleged they had suffered harm in detention on PNG's Manus Island. The government said it was "prudent", but denied wrongdoing.
Australia sends asylum seekers arriving by boat to PNG and Nauru.
The deal is believed to be Australia's largest human rights settlement.
The Supreme Court of Victoria upheld the payout on Wednesday when Justice Cameron Macauley said he was satisfied that A$70m was an appropriate sum.