The Nauruans approached the federal government in a bid to strike a deal to take released immigration detainees, known as the NZYQ cohort, off Australia's hands.
Home Affairs Minister Tony Burke confirmed 30-year visas have been issued to three members of the group who he said had failed the "character test".
The trio were taken into immigration detention after Nauru's intervention prompted the cancellation of their bridging visas.
All three are violent offenders, with one convicted of murder.
"They will be put on a plane and sent to Nauru as soon as arrangements are able to be made," Mr Burke told reporters in Canberra on Sunday.
"That will not be within the next seven days."
Powers were passed in December to allow the minister to pay third countries to take people in immigration detention.
The laws granting that power were in response to the High Court forcing the release of some 200 immigration detainees after ruling indefinite detention was illegal.
Their release caused a political headache for Labor after the coalition seized on alleged reoffending to slam the government for not doing more to keep them locked up following the court's ruling.
Mr Burke argued the trio were not being indefinitely detained and flagged their pending deportation was likely to be legally challenged.
"Lawyers haven't launched anything yet," Mr Burke said.
"Whenever I make any decision, I presume that there'll be a contest in the courts."
Asylum Seeker Resource Centre CEO Kon Karapanagiotidis compared the deportation regime to US President Donald Trump's forcible deportation of migrants to Guantanamo Bay in Cuba.
"Trumpian, immoral and most likely unconstitutional," he called the move in a post on social media.
"The timing of it just before a federal election, it is clear ...the Labor government ... is punching down on refugees, immigrants and people seeking asylum ... and hoping it's going to garner them votes."
Greens senator David Shoebridge said the Albanese government was entrenching a punishing system that treated migrants and refugees unfairly because they were not citizens.
"No one is in immigration detention because they have committed a crime. They are in immigration detention because of a visa issue," he said.
"Today's announcement entrenches a two-class legal system where you can be subject to arbitrary detention and forced to a country you have no connections to because of where you were born.
"What we are seeing is the Albanese government picking and choosing who gets human rights."
Mr Burke, who recently returned from Timor-Leste, suggested more members of the NZYQ cohort could follow suit at the discretion of Nauru.
"Nauru have described these three visas as first three and that's how it should be seen," Mr Burke said.
"On this particular arrangement, the only country that has come to us is Nauru ... and the matter was not discussed at all in Timor-Leste."
He refused to say how much it would cost Australian taxpayers for Nauru to take the three detainees, pointing out it also costs to detain them.
"There was also a cost when they were being held in detention, there was a cost before that when they were being held in prison," he said.
"But no cost has been greater than the cost to the Australian community of their crimes."
Opposition Leader Peter Dutton took aim at Labor's record on immigration, saying the coalition faced another border "mess" if it was returned to power after the upcoming election.
"(But) we're happy to have a look at arrangements that the government's put in place," he said in Darwin.
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