The Manus Island regional processing centre is set to close following a meeting between officials from Papua New Guinea (PNG) and Australia.
Immigration Minister Peter Dutton confirmed the future closure, after meeting with PNG Prime Minister Peter O'Neill yesterday.
Mr Dutton told the ABC no-one from the centre would be resettled in Australia.
He said there was no timeline for closing the centre yet, but both countries would work towards it "as quickly as possible".
"It's important to work through these issues in a methodical way," he said.
"We're talking to third countries at the moment, to look at settlement options."
The ABC understands Australia will give PNG extra resources to cope with the transition, but Mr Dutton would not be drawn on how much.
He said the figure, when finalised, would be substantial.
"We haven't got a final figure on that," he said.
"This Labor legacy of the failed border protection policy, not only did it result in 1,200 people drowning at sea, but it resulted in billions of dollars being spent on this program. It will take years to clean up this mess."
Mr Dutton said there will be savings "in the long run" for the Government.
Mr O'Neill also issued a statement, confirming "both Papua New Guinea and Australia are in agreement that the centre is to be closed".
"A series of options are being advanced and implemented.
"It is important that this process is not rushed but carried out in a careful manner.
"This must take into account the interests of the people of Papua New Guinea and the wellbeing of asylum seekers and refugees."
Shadow immigration minister Shayne Neumann called for Mr Dutton to "secure proper third-country settlement options for refugees".
"It is time for the Turnbull Government to be upfront and honest about what their intentions are with regards to the current situation," the Queensland MP said.
Mr O'Neill called for the closure of the centre in April, after PNG's Supreme Court ruled Australia's detention of asylum seekers on Manus Island was illegal.
According to the latest immigration detention statistics issued by the Department of Immigration and Border Protection in June, 854 men remain on Manus Island.
