"We got them all out," he said in a statement on Thursday.
"This is something the government has been working on for some time, quietly and in a way that would not impact our border protection policies."
The departure of the children and their families brings the number of refugees to have been resettled in the US under a deal with Australia to 493.
Another 265 refugees have been assessed but rejected by the US under its extreme vetting policy.
As the final two refugee families being held on Nauru were scheduled to be transferred to the US on Wednesday, it was revealed once they land they'll have a big financial hurdle to jump.
Under a little known US law, the refugees must pay back to the US government the costs of their and their family's one-way flights there.
For some, touching down at LAX, could cost up to US$12,000 ($16,700).
Refugee Mohammad Yarsir Mubarak - who now lives in San Antonio, Texas, after being held on Nauru - still owes a debt of more than US$7,000 for his family's airfares.
US-based charity AdsUp (Australian Diaspora Steps Up), which pairs Australian expatriates with refugees formerly under Australian care, is trying to help.
Co-founder Fleur Wood told SBS News the reduced social safety net in the US makes debt there hurt more, particularly for refugees.
"A lot of them don't really understand the full extent, and they're very anxious about the debt,” she said, adding a couple of families there have a debt of US$12,000.
“Just seeing that amount of money - they're earning $7 an hour working in a factory and they think, ‘how am I ever going to be able to pay that?’”
Mr Mubarak falls into that category.
He fled Burma after what he says was religious persecution, and now he and his wife have an eight-year-old, a six-year-old, and a three-year-old child.
The three-year-old was born whilst he was detained in Nauru, where he says the Australian government misled him about where he would go, and how long it might take.
He became one of the refugees resettled under the deal struck between the former US administration of Barack Obama and the federal government.
Mr Mubarak says life is the US isn't easy, but it's better than in Nauru.
"Life in America isn't easy, but we have our freedom. And my family has a future,” he said.
“We didn't have a future in Nauru, no life in Nauru."
Ms Wood said the flight costs the refugees have to pay is the normal policy in many countries around the world, not just the US.
Refugees previously held on Nauru and Manus Island have been resettled in 20 different US states. But Ms Wood says what help they are given by the US government once they get there is stretched thin.
"They are given a case manager for the first three months, as a well as a case manager to help them find appointments, help them get a social security card, help them with their healthcare needs, and provide accommodation," she said.
"[But] a lot of those agencies are underfunded, and have way too big a workload. So a lot of our refugees have slipped through the system."
Mr Mubarak, who now works in a mosque in San Antonio, says the help from AdsUp is greatly appreciated, and, despite what he's been through, he has great affection for the Australian people.
"Yes, yes, I am very happy they help us. They help us, they help our family. I am very thankful,” he said.
“I know Australian people. They are very good. I'll never forget. Thank you to the Australian people."
- with AAP