A group of 27 have been selected for resettlement, along with 25 from Papua New Guinea's Manus Island, under Australia's refugee swap deal with the US.
The refugees hail from Bangladesh, Iran, Sri Lanka, Somalia and Myanmar, and are bound for US states such as Arizona, Texas, California and New York.
Ian Rintoul of the Refugee Action Coalition has spoken to the refugees on Nauru, they said they're happy to be finally leaving.
But he says their "hearts and hopes have died on Nauru" where they spent the last several years, having been sent there for offshore processing by Australia.
According to Mr Rintoul, the refugees are expected to pay the US$2000 airfare to the US in monthly instalments over two years.
He said this would be in order to establish a "good credit rating".
Meanwhile, there's no guarantee that the remaining refugees on Mauru and Manus, who number over 1700, will be resettled in the US.
The resettlement deal was originally brokered last year between Australian prime minister Malcolm Turnbull and former US president Barack Obama. The deal agreed on the resettlement of up to 1250 detainees from both Nauru and Manus.
Since taking over the US presidency, Donald Trump signalled he would reluctantly uphold the deal, although it remains unclear how many total refugees from Manus and Nauru will end up in America.
"It has been 10 months since the refugees had their first interviews, and there is no indication of when any more refugees who have applied, will be accepted into the US," said Mr Rintoul.
The refugees had been told by US officials that there was no date for more refugees to fly to the US, and that some people would not be accepted.
"The refugees on Manus and Nauru remain the responsibility of the Australian government," Mr Rintoul said.
"The government should make sure that no one should be left behind. All the people on Manus and Nauru should be brought to the mainland while the government makes arrangements for those who want to go to the USA."
Photo: supplied Nauru refugees