The two leaders signed an agreement on rare earth and critical minerals during a bilateral lunch in the White House cabinet room.
"This is an $US8.5 billion pipeline that we have ready to go," Mr Albanese said while signing the deal as Mr Trump noted it had been negotiated over a period of four or five months.
The agreement involves the processing of minerals, and includes joint investments between the US and Australia, projects in Australia and other joint projects involving Japan.
Australia and the US States will invest about $US3 billion ($A4.6 billion) in critical mineral projects within six months, the White House said.
The US government will also invest in a refinery for the critical mineral gallium in Western Australia.
The prime minister was joined by Resources Minister Madeleine King and Industry Minister Tim Ayres during his visit.
The US president was enthusiastic in his praise for Mr Albanese during the meeting.
"It's a great honour to have you as my friend," Mr Trump said.
"It's a great honour to have you in the United States of America."
Mr Albanese praised the US-Australia relationship and said Mr Trump's work on a Middle East ceasefire was "an extraordinary achievement".
The prime minister went into the meeting hoping to gain assurances the US would not curtail the AUKUS trilateral security agreement, which will deliver Australia nuclear submarines.
The more than $300 billion agreement had been under review by the US Defense Department to ensure it aligned with the "America first" agenda of Mr Trump's administration.
US Navy Secretary John Phelan told the meeting the US and Australia were working very closely to improve the original AUKUS framework for all three parties, which includes the UK, "and clarify some of the ambiguity that was in the prior agreement".
Asked about the submarine deal, Mr Trump said of Australia "they're getting them".
As well, Australia has agreed to purchase $US1.2 billion in Anduril unmanned underwater vehicles and take delivery of a first tranche of Apache helicopters in a separate $US2.6 billion deal, the White House said.
Asked by a reporter about Australia's US ambassador Kevin Rudd's past criticism of Mr Trump, the US president responded: "I don't know anything about him. If he said bad, then maybe he'd like to apologise?".
"Did an ambassador say something bad about me?" he asked Mr Albanese before waving his hand and saying "Don't tell me. I don't want to know".
"Where is he? Is he still working for you?," Mr Trump asked.
Mr Albanese pointed to Mr Rudd who was sitting on the opposite side of the table.
Mr Rudd, who once called Mr Trump a traitor to the west, told the president that happened "before I took this position".
"I don't like you either, and I probably never will," Mr Trump said, as Mr Albanese and the Australian delegation laughed.
Mr Trump said Mr Albanese had invited him to visit Australia and that he was giving the offer serious consideration.
The White House meeting is the first time the leaders have held formal bilateral talks and is the sixth time Mr Albanese has spoken with the US president since he was re-elected in November.
Four of those occasions have been over the phone, while the pair met in person for the first time at a reception hosted by Mr Trump during the United Nations General Assembly in New York in September.
