Labor is tipped to gain the 47 seats it needs to govern in its own right, with the ABC predicting as many as 50 seats going to Labor.
Mr Perrottet said as leader of the parliamentary Liberal Party he took full responsibility for the loss.
"And, as a result I will be standing down as the Parliamentary Liberal Party."
It was clear the party needed a fresh start, Mr Perrottet said, quoting the Labor Party's slogan.
"It is very clear we need a fresh start, we need a fresh start."
Mr Perrottet conceded defeat in a phone call to Mr Minns about 9pm on Saturday.
An early two-party preferred swing of about 6.4 per cent led to decisive calls by analysts on Saturday night.
In his concession speech in Sydney's CBD where Liberal party faithful gathered Mr Perrottet said while elections could get ugly he believed the election was truly a race to the top.
"A genuine, a genuine battle of ideas, and that is when politics is at its best," Mr Perrottet said.
"In many ways, that is due to Chris Minns and of the way that he has carried himself throughout this campaign.
"And that is why I truly believe and have no doubt that he will make a fine 47th premier of NSW I believe he will lead with the same decency and the same integrity that he has led with so far."
The outgoing premier urged everybody across the state to get behind Mr Minns for the sake of the country.
"And ultimately, I ask everybody across NSW, whatever your political persuasion, to get behind him, to get behind him because when New South Wales goes well, our country goes well, and that is something tonight I believe we can all unite behind."
Mr Perrottet, who became premier 18 months ago after Gladys Berejiklian quit amid an ICAC probe, had sought a fourth term for the coalition.
Deputy Labor leader Prue Car said the party had struck a chord with the people of NSW.
"We made a case for change, and we have made the case for change as a team that has done the work," Ms Car told the ABC.
"The campaign, thus far, is showing that we really were listening to people, and talking about the bread-and-butter issues that people are concerned about.
Treasurer Matt Kean said he was not surprised by the result, saying after 12 years of coalition government people were looking for change.
"We we were hoping for the best and preparing for the worst," he said.
The coalition governed for two years in minority with 46 seats, while Labor held 38 seats, with nine crossbenchers, including three Greens MPs.
Both leaders have campaigned hard in vital seats in Sydney's west, where a third of NSW voters live and many electorates are on a knife edge.
Mr Perrottet was flanked by wife Helen as he voted in Beecroft in Sydney's north on Saturday and she was again a fixture as he conceded publicly.
Mr Minns voted in his ultra-marginal southern Sydney seat of Kogarah, flanked by wife Anna and their three sons, and promising a fresh vision for the state.
"Vote for a fresh start for NSW, for a team that's got a plan for essential services, for our schools and for our hospitals, who's going to stand up against privatisation and really put the people of NSW first," he said.
Earlier on Saturday Prime Minister Anthony Albanese lent his support to Mr Minns' pitch for premier, campaigning in the Liberal-held seat of Ryde before casting his own vote at a booth in Sydney's innerwest.
A string of retiring senior Liberal ministers bailing out before the state election showed the Perrottet government didn't even have confidence in itself, he said.
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