Prime Minister Jacinda Ardern was quick to congratulate her left-leaning counterpart, calling Albanese shortly after his victory and reiterating Australia was New Zealand's "most important partner".
So too was National Party leader Christopher Luxon, saying Australia was "New Zealand's closest friend".
Luxon said Albanese was a "good partner for New Zealand" - the pair had met previously when Albanese was infrastructure minister and Luxon Air NZ CEO.
The implications of Albanese's victory for New Zealand remain to be seen, but throughout the campaign he had taken a softer stance on key issues, including immigration, and opposed the Morrison government's bid to increase 501 deportations - a sore point between the countries.
Auckland University Professor of Politics Jennifer Curtin said she was not confident Labor would be very different to the Liberals, given how political the topic was domestically.
One example was how Labor had supported charging those in detention awaiting deportation fees, said Curtin, an Australian politics expert and dual citizen.
Another area of contention was around China, with the prevailing view across the Tasman New Zealand was "soft on China", and particularly the response to the security pact with the Solomon Islands.
Throughout the debates, incumbent Marisa Payne and shadow minister Penny Wong had taken similar stances, seeing China as using "economic coercion and being quite aggressive".
"The Morrison government was seen to have lost face [with the Solomons deal] and they have spoken a lot more harshly about China than our government," Curtin said.
Potential areas of common ground included climate change, and particularly how to tackle the issue in the Pacific region, with Ardern seen globally as a leader in the space and having labelled it her generation's "nuclear free moment".
In contrast to Morrison, who in 2018 campaigned backing coal, Albanese's popularity has also been linked to a strong stance on climate action.
"So it could be valuable for the region for these two countries' leaders now to be on the same page on climate change," Curtin said.
Albanese has also, at least in rhetoric, made strong statements on indigenous rights, including referencing the Uluru Statement in his first speech since victory was announced, which calls for a First Nations voice in the constitution.
Wong also spoke during the campaign about establishing a First Nations ambassador, and putting an indigenous lens across the foreign affairs portfolio to change how Australia spoke to the rest of the world - similar to work by New Zealand Foreign Minister Nanaia Mahuta.
Emeritus Professor of Politics and International Relations at Macquarie University Murray Groot told Newstalk ZB there were lessons to be learned about Morrison's loss, which has been linked to his management of the pandemic, and current inflation and cost of living issues.
People had "taken for granted" any of the good work, and were now just focused on the costs, the lockdowns, lost jobs and inability to travel, he said.
"They tried to push the narrative that we are now through it ... but that hasn't worked."
Cost of living issues and inflation, wages falling behind, came to the forefront too, along with a lack of action on climate change, he said.
New Zealand had not featured prominently in any of the debates, and on 501s Groot said he not expect Australia to "make a big issue" over it.
"But I think there is room for New Zealand to renegotiate."
Community Law Centres O Aotearoa CEO Sue Moroney meanwhile says the change in government should hopefully a more progressive stance on asylum seekers and rights of New Zealanders living in Australia, including 501 deportees.
She said changes back in February 2001 when Australia removed its direct pathway to citizenship for New Zealanders had seen them excluded from social security and housing measures, and led to disproportionate deportation laws.
"The injustice of this situation has affected thousands of lives both here and in Australia as families have been torn apart by these policies," Moroney said.
"The results are played out on our streets every week, with the changing nature of the crimes committed in New Zealand.
"Australians have spoken for a change in the Government they want. It was significant to see that a last-ditch attempt to frighten Australians to vote for the status quo by using the threat of asylum seekers didn't work. "
"This shows a mood change in Australia that two Australasian Labour Prime Ministers can respond to. In the meantime, we urge the NZ Government to improve services and support for those deported by Australia under their current draconian laws."
