Declaring victory at Labor headquarters in Sydney, the prime minister said serving as prime minister was the greatest honour of his life.
"It is with a deep sense of humility and a profound sense of responsibility that the first thing that I do tonight is to say 'thank you' to the people of Australia for the chance to continue to serve the best nation on Earth," he told supporters.
"Today, the Australian people have voted for Australian values: for fairness, aspiration and opportunity for all.
"Australians have voted for a future that holds true to these values, a future built on everything that brings us together."
Large swings to the government across several states and many electorates in Liberal heartland will mean Labor governs in its own right with expanded numbers in parliament.
With almost 40 per cent of the vote counted, Labor is set to win 87 seats, an increase from the 78 it achieved going into the election.
With the election win, Mr Albanese is the first prime minister since John Howard to win back-to-back elections.
Among the gains for Labor was Opposition Leader Peter Dutton's seat of Dickson in Queensland.
It's the first time an opposition leader has lost their seat in a federal election, with Mr Dutton losing to Labor's Ali France.
Conceding defeat, Mr Dutton said the election was not the result the coalition was after and accepted full responsibility for the party's loss.
"We didn't do well enough during this campaign, that much is obvious tonight," he told party supporters in Brisbane.
"I've always wanted in public life for the best for our country and the best for every Australian.
"It's an historic occasion for the Labor Party, and we recognise that."
Mr Dutton also apologised to other coalition members who lost their seat on election night.
"There are good members, good candidates, who have lost their seats or their ambition, and I'm sorry for that," he said.
"We have an amazing party and we'll rebuild."
With the election loss, the coalition is on track to one of its lowest ever primary votes since the party was formed in the 1940s.
Labor has picked up marginal seats such as Leichhardt in Queensland, Bass in Tasmania and Sturt in Western Australia.
But it could lose the formerly safe seat of Bean in the ACT to an independent, with the result still being too close to call.
Treasurer Jim Chalmers said voters had comprehensively rejected the policies of the coalition under Mr Dutton's leadership.
"The nuclear stuff was bad for Peter Dutton. He made an egregious error on the Sunday night of the final week, saying he would be comfortable having a nuclear reactor in his suburb," he told ABC.
Coalition campaign spokesman James Paterson admitted anger from voters against US President Donald Trump had been a drag on support for right-wing parties.
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