The party picked up 12 per cent of the primary vote in the House of Representatives and 13.9 per cent in the Senate, with almost 2.2 million Australians casting ballots for Greens candidates.
If the trend continues, the Greens will hold 12 seats in the Senate.
And there could be Greens MPs in as many as five lower house seats.
Party leader Adam Bandt has been returned in his seat of Melbourne.
But he could be joined by MPs for Ryan, Griffith and Brisbane in Queensland, and Macnamara in Victoria.
As counting continued on Sunday, the party was slightly under a Senate vote "quota" in NSW, Queensland and South Australia, having held its seats in Victoria, WA and Tasmania.
Mr Bandt said the result was a mandate for action on climate and inequality.
"We want to work with Anthony Albanese to deliver the stable, effective, progressive government that Australians have voted for but he will need to work constructively with the Greens and the rest of the cross bench," he said.
He said Greens preferences had been critical to unseating many coalition candidates.
"This was a greenslide," he told reporters in Brisbane.
Australian Conservation Foundation chief Kelly O'Shanassy said there was a clear vote for bolder climate action.
"Labor has committed to cut climate pollution by 43 per cent this decade but we know the science demands the new government go further if we want to have a safe climate," she said.
The ACF has called for quick action on improving pollution caps and baselines to cut emissions by Australia's biggest polluters, restoring the role of the Climate Change Authority to advise government, stronger nature laws and a new national Environment Protection Authority.
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