Mr Turnbull confirmed the refugees would head to the United States in the “first stage” of the deal.
He said “a large number” of the remaining refugees were currently undergoing “extreme” vetting by US immigration authorities.
“There are many that are being vetted but it is entirely up to the United States as to how many are taken,” Mr Turnbull told Seven’s Sunrise program on Wednesday morning.
The announcement is the first instance of the US accepting refugees from within Australian detention under a deal Australia first brokered with president Barack Obama.
The agreement, which president Trump slammed as a “dumb deal” early in his presidency, could see the US take up to 1,250 refugees – although both leaders have stressed the US has ultimate discretion.
In a leaked transcript of his first phone call with Mr Turnbull, Mr Trump questioned whether one of the refugees would “become the Boston bomber in five years”, referencing a deadly terror attack.
“I just want to thank again president Trump for continuing with that arrangement,” Mr Turnbull said on Wednesday.
Some of the refugees received appointment slips on Tuesday afternoon.
“People are a bit surprised, some people had given up hope that it would happen," Refugee Action Coalition spokesman Ian Rintoul told AAP.
The government has promised to close the Manus Island detention centre by the end of October.
A document on a notice board on Manus Island warns refugees every case is different and moves through the required process at different speeds.
“Please be patient,” the US Resettlement Support Centre document says.
It says more decisions will be issued over coming months.
With AAP.