The fire on the remote ocean rig raged for three days, sending flames hundreds of metres into the air.
Australasia, said it had pumped 3,500 barrels of mud into a second relief well to cap the leak.
The rig had been leaking 400 barrels of oil a day into the ocean for the past 10 weeks before the fire broke out Sunday. It has caused a massive oil slick to spread across the previously pristine waters of the Timor Sea, threatening marine life.
The premier of the state of Western Australia, Colin Barnett, said the fire and oil leak raised serious safety concerns about plans to pipe gas 800 kilometres from the ocean gas fields to Darwin.
The Australian government has ordered a inquiry into the disaster.