The October 20 bilateral with the US president in Washington was confirmed by Mr Albanese during a doorstop on the sidelines of the United Nations General Assembly meeting in New York.
The confirmation also came as Australia's Ambassador to the US Kevin Rudd earlier told those attending a speech by Mr Albanese in New York that it was on and that Australia was "delighted".
Mr Albanese stressed that Mr Trump had agreed to a meeting "some time ago".
"We had another chat about it on the phone and we'll have a meeting in Washington DC on October 20," he told reporters.
The prime minister has been battling for formal face time against other world leaders after missing out on a hoped-for meeting with Mr Trump during the UN leaders gathering.
In the meantime, Mr Albanese could get a quick hello with Mr Trump when he attends a reception hosted by the president and First Lady Melania Trump on Wednesday morning (AEST) on the sidelines of the UN gathering.
Australia was left off the president's official schedule this week, which includes bilateral meetings with the leaders of Ukraine, Argentina, Egypt, Pakistan and Turkey.
Some analysts had suggested the federal government's decision to formally acknowledge Palestine may have contributed to this week's snub.
Others said it might have been a blessing in disguise.
Meetings with Mr Trump were often transactional and coercive, which could be risky for Mr Albanese, Perth USAsia Centre chief executive Gordon Flake said.
"With the world on fire, I think there are other bigger priorities we have than just a one-on-one with President Trump," Professor Flake told AAP.
"I understand anxiety about ... not yet having a leader-to-leader summit, but at the same time, if you begin to ask the question 'what do you want from the summit', I think we're in a pretty good position.
"There's no abiding, immediate crisis that we're trying to solve."
During Mr Albanese's speech at the event hosted by Australia's Macquarie Group, he showcased Australia to global investors, focusing on Labor's multi-billion-dollar suite of "future made in Australia" policies.
Mr Albanese also might brush past Mr Trump at next month's APEC and ASEAN summits in South Korea and Malaysia, respectively.
The opposition had been highly critical of the prime minister's failure to secure a meeting with the US president, given the pair have important issues to discuss such as Mr Trump's sweeping tariffs and the AUKUS nuclear submarine deal.
"It's not good that over 30 world leaders have had physical, face-to-face meetings with the US president and our prime minister hasn't," opposition trade spokesman Kevin Hogan told AAP on Tuesday.
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