Nauru has agreed to an arrangement with the Australian government to accept three non-citizen residents on long-term stay visas, free of detention centres, to remain on the tiny Pacific island.

The Commonwealth said in a statement that a Memorandum of Understanding stemming from a previous interim agreement to grant the asylum seekers who had "no right to remain in Australia but who were not able to be returned to their home country" the ability to live freely in Nauru.

The Micronesian nation has processed and housed thousands of asylum seekers dating back to 2001, since shortly after the Australian navy intercepted the Tampa.

However, the Department of Home Affairs in Canberra declined releasing its Memorandum of Understanding under Australia's Freedom of Information Act, which has grounds to exempt document disclosure over its ability to adversely "maintain good working relations" with Nauru.

The latest deal of Nauru taking on the new residents - along with a return of asylum seekers to its shores but inside Nauruan detention centres - is reportedly worth $2.5 billion in payments from the Australian government for the next 30 years.

The fund is separate from Nauru's one-off $20 million establishment fee and a run of additional annual payments towards operational costs of the detention centres.

Nauru has struggled this century to find income streams for the nation's 12,000 residents since the collapse of its phosphate industry that once made the 21-square kilometre microstate one of the richest states in the world, per capita.

"The arrangement reaffirms Nauru and Australia's shared commitment to humane, lawful, and the mutually-respectful management of migration and settlement," Nauruan Deputy Minister for Internal Affairs, Tawaki Kam, said in a statement. "And the establishment of a second trust fund embodies the government's pursuit for economic resilience."

"The settled persons will enjoy freedom of movement, equal treatment, and access to essential services in accordance with Nauru's international obligations and human rights commitments."

Australian Minister for Home Affairs, Tony Burke, has not revealed how many asylum-seekers were involved in the initial transfer outside of the three new Nauruan residents.

Australia's Human Rights Commissioner has issued a stern warning that the deportations to Nauru, under Australia's new deal signed last week, exposes a disturbing lack of transparency and raises serious human rights concerns, under the United Nations charter.

"This development marks the beginning of a removal arrangement still shrouded in secrecy," Human Rights Commissioner Lorraine Finlay said

"The lack of confirmation about even this most basic detail of the transfer underscores a secrecy surrounding the arrangement and raises questions about the (Commonwealth) government's commitment to transparency and so to accountability."

While the only publicly available information says the agreement includes commitments by Nauru to ensure treatment is "in accordance with international human rights law", it is not clear how those commitments will be enforced, what recourse individuals will have if their rights are breached, and what procedures are in place to facilitate independent oversight and monitoring.

Commissioner Finlay said Australians have a right to be aware how their taxpayer-funded money is being spent in the name of the "basic principles of transparency, accountability, and fairness".

"The lack of clarity around these questions is deeply concerning," she said.

"The Australian government needs to ensure any arrangement is consistent with our domestic and international human rights obligations.

"As the UN Human Rights Committee has made clear, outsourcing the management of asylum seekers and refugees does not absolve a state of its legal responsibilities.

"The decision to deport individuals under an opaque deal reportedly worth billions undermines the principles of accountability and transparency that should underpin our immigration system.

"Australia has the right to manage its borders and make decisions about removal, but how we do that matters."