But the federal Resources Minister Keith Pitt is unimpressed.

Equinor said the proposed oil drilling was no longer deemed "commercially competitive".

"We will engage with the federal and state authorities regarding our decision to discontinue the exploration program," the company's local boss Jone Stangeland said on Tuesday.

"We hold an exploration permit offshore Western Australia and will maintain other ongoing interests and activities in Australia."

Mr Pitt is disappointed by the decision and is encouraging other proponents to fill the void.

"I know many will find Equinor's decision not to proceed with this oil exploration project in the Great Australian Bight extremely disappointing, and it is particularly hard for South Australia," he said.

"The Bight Basin remains one of Australia's frontier basins and any proposals for new oil and gas fields in this area will be assessed fairly and independently."

The Australian Petroleum Production and Exploration Association is also gutted, saying the project could have shored-up local energy supplies and eased Australia's reliance on imported oil.

Australia's independent regulator approved the oil drilling in December.

An earlier study found oil exploration in the Great Australian Bight could create 2000 jobs and generate more than $7 billion in annual tax revenues.

Greenpeace and others have welcomed the withdrawal as "a win for the environment".

"This is an incredible win for people power and nature after years of relentless campaigning by coastal communities, indigenous traditional owners, surfers, the seafood industry, tourism operators and other local businesses," chief executive David Ritter said.

The Environmental Defenders Office has been representing the Wilderness Society in a bid to overturn Equinor's environmental approvals.

The EDO has hailed the legal action as a factor in Equinor's decision, saying the company would have had to go back to the drawing board if the move was successful.

The case is due to appear in the Federal Court next week but may no longer be necessary.

BP, Chevron and Karoon Gas have all withdrawn from the Bight but Santos, Murphy Oil and Bight Petroleum still have plans to drill there.

"The only way to protect coastal communities and the Great Australian Bight's unique marine life is to rule out drilling permanently," Mr Ritter said.

"The Australian government should now impose a permanent moratorium on oil drilling in this precious marine wonderland."

Australian Associated Press