Whether Trump honours the deal Australia reached with the outgoing Obama administration, and announced earlier this month, will provide an early test of Trump's anti-immigration stance.
Campaigning for the presidency, Trump had started by advocating a blanket ban on Muslims entering the United States, but later adjusted his stance to propose that the ban should apply to people from nations that had been "compromised by terrorism".
Australia's Prime Minister Malcolm Turnbull said on Sunday that the United States had agreed to take a "substantial" number of those held on Manus Island and Nauru. Many of them are Muslims who have fled conflicts in Iraq, Syria, Afghanistan and Pakistan.
Under Australia's tough border security laws, asylum seekers intercepted trying to reach the country by boat are sent for processing at the camps on Papua New Guinea's Manus island and Nauru.
The resettlement deal with United States came after Turnbull's government agreed in September to accept people from Guatemala, Honduras and El Salvador as part of Australia's annual intake of 18,750 asylum seekers, to support a resettlement plan for Central Americans drawn up by Washington.
Turnbull said on Monday the first refugees to be resettled in the United States will not come before the Jan. 20 inauguration of President-elect Trump.
"The process will continue for some months. The United States won't be short-cutting their security or health checks," said Turnbull.
Analysts said the timing could prove awkward for Turnbull.
"It looks pretty clear that the resettlement deal was done as a quid pro quo after Australia agreed to resettle Central American refugees," said Peter Chen, professor of political science, University of Sydney.
"But by holding off and starting the process in the expectation that Hillary Clinton would win the U.S. presidency, it gives Trump the ability to reject the deal."
Over the weekend, Trump said his administration would deport up to 3 million immigrants in the country illegally who have criminal records. While campaigning, Trump said he would deport 11 million illegal immigrants.
Should Trump veto the deal with Australia, the detainees would be left with the choice of returning to their home countries or remaining in Nauru or Papua New Guinea.
A veto would force Turnbull to search for another country willing to take them while facing growing outrage both at home and internationally over the treatment of the refugees.
Turnbull said he remained confident that the new U.S. administration would stand by the deal, stressing that it didn't require any increase in the United States' annual intake of asylum seekers.