It will be the first summit between the security allies since Trump's second election.
The two leaders have much to discuss, including the multi-billion dollar AUKUS project, also involving Britain, to provide Australia with nuclear-powered attack submarines to counter China's ambitions in the Indo-Pacific. The project is currently under Pentagon review.
"Australia and the United States are great partners. I expect it to be very constructive," Albanese said in New York on Tuesday, confirming the meeting.
He later posted a selfie photograph to Instagram of the two leaders together at a reception in New York on Tuesday evening, writing: "Good to chat with President Donald Trump at US welcome reception for world leaders".
Albanese is attending the United Nations General Assembly for the first time, where he recognised Palestinian statehood on Monday. He will promote Australia's ban on social media for children tomorrow, and seek support for Australia and Pacific Island nations hosting the COP31 climate summit amid resistance from Turkey.
Reelected as leader of a centre-left Labor government in a May national election, Albanese had been criticised by domestic political opponents because he has yet to meet Trump, after a meeting scheduled on the sidelines of the G7 summit in Canada in June was cancelled when the president left early.
US Under Secretary of Defense Elbridge Colby, a public critic of AUKUS, is leading the Pentagon review. He said last year that submarines were a scarce, critical commodity, and US industry could not produce enough to meet American demand.
On Tuesday, a senior US State Department official said he understood the review would be completed in the autumn, and involved wide coordination between the Pentagon, the State Department and other agencies.
"Ultimately, what this is about is making sure that AUKUS benefits America and that the United States Government writ large is in full support behind it," the official said.
Australia, which has already paid about $1 billion ($NZ1.7 billion) as part of ongoing contributions to support the expansion of American submarine shipyards, has maintained it is confident AUKUS will proceed.
Under pressure from Washington to increase defense spending, Australia this month announced an extra $12 billion to upgrade a shipyard in Western Australia for AUKUS submarine maintenance.
