The prime minister and Mr Trump came face-to-face after Mr Albanese arrived at the evening event in New York with fiancee Jodie Haydon on Wednesday (AEST).
No media were allowed access at the exclusive gathering but Mr Albanese posted a photo of the pair to his Instagram just before 3am New York time.
About 145 leaders and their partners lined up for hours to get a picture with Mr Trump and First Lady Melania Trump.
Earlier, a formal sit-down was locked in for the pair following months of speculation and several phone conversations between the two leaders.
During a press conference on the sidelines of the UN meeting, Mr Albanese confirmed the October 20 talks would take place at the White House.
Australia's ambassador to the US Kevin Rudd told those attending an infrastructure-themed speech by the prime minister that the government was delighted at the confirmation.
Mr Albanese will hope to receive the 79-year-old in a less belligerent mood than at the UN.
The Republican delivered a combative 56-minute speech on the floor of the UN, arguing for lower levels of global migration and a turn away from policies to combat climate change.
He strongly criticised moves by allies, including Australia, to support a Palestinian state.
Asked about Mr Trump's address, Mr Albanese said it was good to hear his views.
"It was a great privilege to be at the United Nations this morning to hear President Trump and other leaders ... put forward their perspectives," he told reporters.
US ambassador to Israel Mike Huckabee said his nation had "strong disagreement" with the countries he described as calling unilaterally for a Palestinian state.
"It is having the opposite effect of what I think these countries want ... they want to see an end to (conflict in) Gaza. This is prolonging it," he told ABC Radio.
"The number of countries have decided to jump on this wagon, I just don't know what they expect they're going to get from this other than more turmoil."
Former foreign minister Bob Carr said recognition signalled "equal humanity" for Palestinians as the same basis of respect given for Israelis.
"The message is, to Israel, stop the genocide, a brazen breach of the convention, and stop the settlement expansion on the West Bank," he said.
The October 20 meeting confirmation will calm hostilities from the opposition, which have criticised the prime minister's failure to secure a bilateral until now.
During his speech at the event hosted by Australia's Macquarie Group, Mr Albanese showcased the nation to global investors, focusing on Labor's multibillion-dollar suite of "future made in Australia" policies.
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