Well control experts aboard the West Triton rig pumped about 3400 barrels of heavy mud and 1000 barrels of brine down the relief well into H1.
During a media briefing, PTTEP Australasia director Jose Martins said he was relieved the operation had succeeded but warned that the mud was a temporary measure and there was still a long way to go before the well could be fully secured.
He added the priority was now to determine the best method of plugging the well.
"We do not underestimate the significantly increased technical complexity, logistical challenges and hazards of the work now required in the wake of the damage caused by the fire to the well head platform and the West Atlas rig," Martins said.
Federal Resources Minister Martin Ferguson said a commission of inquiry into the incident and a commissioner would be announced before the end of the week, while the National Offshore Petroleum Safety Authority said it would carry out its own inquiry.
The West Australian quoted Ferguson as saying that the industry had learnt much during the 74-day operation.
"We have had to respond to a lot of challenges and we've met every single one."
The Australia Petroleum Production & Exploration Association congratulated those who had worked to seal the well and said the industry strongly supported the inquiry into the leak and subsequent fire to determine what happened and why.
Martins said PTTEP remained committed to fully funding the spill cleanup and environmental monitoring, and would fully cooperate with the inquiry.
The Greens also welcomed the news that the leak had been plugged and called for the inquiry to start immediately.
The company added that while some material on the topside of the West Atlas might still be on fire, this was expected to burn out as the fuel source ran out.
The well will be monitored for the next 24-48 hours to ensure it remains stable.
PTTEP will also present a safety case revision to the National Offshore Petroleum Safety Authority to reboard the platform to assess the damage and plan for the next phases of the operation.
The company will consider spraying the wellhead platform with seawater to help cool it before reboarding.
While it is still too early to know the extent of the damage, the company noted that the cantilever portion of the West Atlas had buckled during the fire and was resting on top of the wellhead platform.
PTTEP added that it had spent at least $170 million since the leak started in August and was preparing an insurance claim to recover that amount.