A photograph released by PTTEP's Australia arm showed the rig smouldering after the fire was extinguished.
"The company declared a shutdown or "well kill" was completed at approximately 17:15 CST [08:45GMT] today," PTTEP said in a statement.
"The well continues to be monitored and a mixture of light mud and brine is continuing to be pumped into the relief well to maintain a stable situation."
Tuesday's operation to stem the flow of oil was the fifth attempt to plug the leak that had created a slick threatening sealife across thousands of square kilometres.
On Monday, PTTEP said that part of the rig had already collapsed onto the wellhead platform as specialist fire crews continued efforts to extinguish the blaze.
The Australian government said on Tuesday that PTTEP was "under a lot of pressure" to control the blaze and stop the flow of oil which activists say has caused a catastrophe for the marine environment.
"It's clearly had an impact on the standing of the oil and gas industry in Australia," Martin Ferguson, Australia's minister for resources and energy told ABC Radio.
Ferguson said that once the spill was contained, he would launch an inquiry and, if the rig operator was "found to have been at fault with respect to any of their responsibilities, then any potential action will be appropriately considered at the time".
The rig began leaking oil on August 21, spewing between 400 and 2,000 barrels of crude into the Timor Sea each day.
According to the WWF environmental campaign group, hundreds of seabirds have died after coming into contact with the toxic slick, while dolphins, whales and other marine life are also being exposed to the spill.
Green groups say the environmental impact could last for another 20 years
Paul Gamblin, a WWF policy advisor based in Australia, said the spill had produced a "chemical cocktail" that could have a long-term impact on the region's wildlife.
Speaking to ABC radio, he said the area around the rig was a "very near pristine environment" which had now been contaminated with upwards of five million litres of toxic substances.
On Tuesday, Senator Bob Brown, the head of Australia's Green party, repeated calls for the government to take tougher action and demanded Martin Ferguson's resignation over his handling of the incident.
"He has completely bungled one of the biggest environmental catastrophes the Commonwealth government has had to deal with," Brown told local media.
"He is an oil industry parrot and he should resign."
Ferguson said previously that the oil would "evaporate naturally" and that he was proud of the oil industry's environmental record.