Mr Trump nominated David Brat for the position, which had been vacant since 2024.
Mr Brat represented Virginia's seventh congressional district in the US House of Representatives for the Republicans.
He made headlines after defeating incumbent US House majority leader Eric Cantor, one of the highest-ranking politicians in the nation, in a primary election to be the Republican candidate for the seat in 2014.
A member of the Tea Party movement, he was elected to the House of Representatives later that year and served two terms.
He lost his seat at the 2018 elections to Democrat Abigail Spanberger, who now serves as Virginia's governor.
After leaving congress, he was named dean of Liberty University's school of business in Virginia.
A self-described "free trader", Mr Brat has more recently defended the president's punitive tariff regime, arguing the import taxes were needed to counter other countries' unfair trade practices.
The ambassador position is yet to be finalised as the appointment needs to be ratified by the US Senate.
Prime Minister Anthony Albanese said the US-Australia alliance would remain strong, regardless who was in the ambassador role.
"I'll work with whoever is determined to be the ambassador. That is a decision for the United States," he told reporters in Canberra on Tuesday.
"We respect the sovereignty of countries to put forward ambassadors, just like we expect our choices to be endorsed."
Opposition Leader Angus Taylor said he welcomed the appointment by Mr Trump.
"He sounds like he has a great background, very focused on economics. We need to restore our standard of living and protect our way of life in this country and it's good to have someone from the US who understands a lot about that," he told Sky News.
"We've got to nurture that alliance and strengthen it. I think it can remain strong, independent of who is the president at any particular point in time, as long as we remain committed to it."
If successful in his selection, Mr Brat will succeed Caroline Kennedy.
Ms Kennedy, the only surviving child of former Democratic president John F. Kennedy, was appointed under the Biden administration.
Mr Trump had not appointed an ambassador to Australia throughout the first year of his presidency, a similar situation to his first term when it took him almost three years to nominate someone.
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