Uranium will be shipped from Australia to India, ending more than a decade of delays to regular shipments of the fuel despite the two nations signing a historic nuclear co-operation pact.
Australia and India signed a civil nuclear deal in 2014 but regular shipments of uranium haven't occurred amid concerns the fuel could be used for weapons.
Growing partnerships between the two nations have prompted a fresh deal to be signed.
"While we are separated by an ocean, we are indeed the closest of friends," Mr Albanese told reporters in Melbourne.
The Indian prime minister will later on Thursday address 30,000 members of the Indian-Australian community in what is expected to be a loud rally at Melbourne's Marvel Stadium.
"Australia's relationship with India has never been more consequential than it is today," Mr Albanese said of the countries that are six years into a comprehensive strategic partnership.
A joint maritime security road map has been endorsed, along with plans to boost the coast guards of both nations.
Australia's Cocos Keeling Islands, which sit largely untouched in the Indian Ocean, will be used for a temporary space-tracking terminal as part of India's space plans.
Further education deals were announced, including approval for a Flinders University campus in India and increased Australian vocational programs in the Asian nation.
In 2026, 41 projects will receive $10 million worth of funding through the Centre for Australia-India Relations.
Mr Modi said a "common world view" helped the countries continue moving forward with deep trust for each other, particularly in sharing education.
That view was also shared with Canada, which will join a three-way technology and innovation partnership for work on emerging technologies including artificial intelligence.
While few national leaders can draw a crowd of tens of thousands during an international diplomatic visit, the Indian leader is an exception.
Members of the Indian diaspora across Australia have travelled to Melbourne in large numbers for a glimpse of the leader of the world's most populous nation.
Mr Modi was one of three types of people who were "very popular" in his homeland, Canberra India Council chair Deepak-Raj Gupta said.
"Politicians, Bollywood stars and cricket players,'' he said.
"It doesn't really matter who you are if you fall into one of those."
Mr Gupta has travelled to Melbourne with his wife and a contingent of friends to attend as many Modi-related events as possible.
But Mr Modi is also one of the world's most polarising political leaders.
Human rights groups such as Amnesty International have condemned him for declines in India's living standards and for targeting journalists and academics through anti-terror legislation.
Marginal religious groups including Muslims and Christians have also been targeted.
Nevertheless, Mr Modi was able to unite the Indian diaspora in a way no one else could, Australian Multicultural Action Network president Ravi Krishnamurthy said.
"We look for connection (between Australia and India). There is pride in adding to Australia's multicultural community," he said.
Mr Krishnamurthy said he hoped there would be more conversations about two-way trade and tertiary education deals.
"Businesses here are starting to invest in India," he said.
The Australian Federal Police formally warned a young person who had made a death threat towards Mr Modi ahead of his arrival in Australia.
A far-right influencer also gatecrashed the Melbourne hotel where the Indian prime minister is staying, before being thrown out by police.
He posted a video of his late-night tirade where he yelled "f*** Modi" in the hotel's lobby.
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