The federal government and energy company Asset Energy agreed to end their legal battle over Mr Morrison's decision, by proposing consent orders to the Federal Court.
Asset Energy launched a legal challenge to the PEP-11 decision last year, saying Mr Morrison had breached the requirements of procedural fairness and that he was not validly appointed as the responsible minister of the joint authority.
Mr Morrison used additional powers he had gained by swearing himself in as resources minister to intervene in the PEP-11 decision and veto it in 2021.
Petroleum Exploration Permit 11, known as PEP-11, is a petroleum well off the NSW coast between Wollongong and Newcastle, covering about 8,200 square kilometres.
If the court accepts the orders, Mr Morrison's decision would be overturned and put back to the Commonwealth-NSW Offshore Petroleum Joint Authority for consideration, the government said on Friday.
The federal and NSW state governments are both members of the decision-making authority.
The former prime minister and MP for Cook has been criticised and censured for secretly taking on five portfolios when he was prime minister.
Resources Minister Madeleine King said she was glad the government was able to reach a resolution with the energy company.
"I assure Australians that any decisions that I take as the federal minister for resources will always be based on sound evidence and in accordance with the law," she said.
"Australians quite rightly expect this of their elected leaders.
"I am not going to provide an ongoing commentary on future official decisions that come before the Joint Authority, whether in relation to PEP-11 or any other matter."
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