Mr Trump claimed victory in the US election on Wednesday over Kamala Harris in a comeback victory after several swing states were called in favour of the Republicans.
He will be the first US president to serve non-consecutive terms in office since Grover Cleveland in 1892, defying the odds to return to the White House after being criminally convicted.
Foreign Minister Penny Wong says we shouldn't be surprised if things change in the US under Trump. (Mick Tsikas/AAP PHOTOS)
Foreign Minister Penny Wong said Australia and the US would continue to work closely together, despite Mr Trump indicating he would pursue a new path.
"President Trump has run a campaign based on change ... he's made it clear he's going to do things differently, so we shouldn't be surprised as things change," she told ABC Radio on Thursday.
"But equally, Australia should be confident in ourselves, in our place in the world and our ability to work together to deliver on our interests. We'll certainly be doing that."
Senator Wong said while the federal government had not yet been in contact with the incoming president, officials were looking to get in touch soon.
Donald Trump claimed victory in the US election on Wednesday evening. (Mick Tsikas/AAP PHOTOS)
The foreign minister indicated the alliance between the countries would be strong, despite policy differences likely to emerge.
"It's an alliance which has, throughout its history, have been times where leaders and governments have disagreed," she said.
"The previous Trump administration withdrew from global commitments on climate, we did not do so.
"We will continue to work with the new administration and the alliance is big enough and strong enough to deal with differences. Ultimately we share a high degree of alignment in strategic objectives."
Prime Minister Anthony Albanese said the election marked an important moment for Australia and the Asia Pacific region, and vowed to work closely with the Trump administration.
"Australia and America are old allies and we are true friends," he said.
"Our nations are bound by a history of shared sacrifice, a commitment to common values and - above all - enduring respect and affection between our peoples.
"I look forward to talking with President Trump and working with him in the best interests of both our nations."
Opposition Leader Peter Dutton also extended his congratulations to the Republican leader on behalf of the federal coalition.
Opposition Leader Peter Dutton hailed Mr Trump's victory. (Mick Tsikas/AAP PHOTOS)
He described the US as an "overwhelming force for good", declaring the world was at its best when Australia's close ally was strong and at its best.
Former prime minister Malcolm Turnbull, who was in office during Mr Trump's first term as president, said Mr Albanese needed to stand up for Australia's interests.
"He's unconventional in the sense that the only real decision maker in his White House was and will be himself," he told ABC Radio.
"You can have very good ambassadors and very good officials ... but ultimately, the deals are going to be done between the Australian prime minister and the American president, and so that personal relationship has got to be grounded in respect.
"What Trump respects is strength, so if you suck up to Trump, you'll just have to do more sucking up."
People joined watch parties across Australia as the US election unfolded. (James Ross/AAP PHOTOS)
Opposition foreign spokesman Simon Birmingham said it was critical the alliance between the countries ensures the AUKUS deal, in which Australia would acquire nuclear submarines from the US, still goes ahead.
"What we should be doing first and foremost is ensuring that President Trump and his incoming administration understand just what a mutually beneficial agreement AUKUS is to start with, as it has successfully been negotiated," he told ABC Radio.
"This is something that enjoys strong bipartisan support in both of our countries."
Greens leader Adam Bandt said Mr Trump's re-election was a "bad day for the world", including women, people of colour and members of the LGBTQI community.
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