Greens-backed independent Alexander Van der Bellen, 72, swept 53.6 percent of the votes, while his rival of the anti-immigration Freedom Party (FPOe) received 46.4 percent, projections showed.
The head of Austria's far-right Freedom Party (FPOe) on Sunday ruled out launching a legal challenge against the defeat of the party's candidate Norbert Hofer in the presidential election.
"This time clearly there are no complaints... Today we can be sure that citizens' votes were properly handled," Heinz-Christian Strache said on public television. In May the FPOe successfully challenged Hofer's defeat and secured a re-run.
"I would like to take this opportunity to congratulate Mr Van der Bellen," FPOe chief strategist Herbert Kickl told Austrian media.
Hofer has conceded defeat. Photo: Shoshana Rae Stark
The official result of the marathon election, which lasted nearly a year, is not expected before Monday when postal votes will be tallied.
But the Freedom Party conceded defeat within minutes of the poll projections being released, shortly after voting ended.
The outcome deals a crushing blow to Hofer who already narrowly lost to Van der Bellen, 72, in a first runoff in May, an outcome that was contested by the FPOe and eventually annulled over ballot counting breaches.
"From the start I have always fought and argued in favour of an Austria that is pro-European," a visibly relieved Van der Bellen said on public television.
"If the projections are right, the Austrian election result will be a clear victory for common sense against right-wing populism," said Germany's Vice Chancellor Sigmar Gabriel.
Smooth-tongued gun enthusiast Hofer had vowed to "get rid of the dusty establishment", seek closer ties with Russia and fight against "Brussels centralising power".
Observers had feared that a win for the Austrian far-right could trigger a domino effect with key elections next year in France, Germany and The Netherlands.
"Congratulations to the FPOe which fought bravely. The next elections will be theirs," tweeted the FPOe's French ally Marine Le Pen of the National Front, who is running for president in 2017.
His defeat will also see EU leaders breathe a sigh of relief in the wake of the anti-establishment tide sweeping many countries following Brexit and Donald Trump's shock election victory in the US.
Populist surge across Europe
Populist groups across Europe, on the right and the left, have benefited from a growing sense of unease about globalisation, multiculturalism, rising inequality, and austerity cuts.
The Austrian vote is being held on the same day as a high-stakes referendum in Italy, which could bring about the resignation of its prime minister and renew chaos in a bloc already weakened by Britain's shock vote in June to quit the EU.
Here's a loose translation of the Facebook concession from Hofer:
I would like to thank you. You have given me such great support, and I am incredibly sad that it didn’t work out. I would have liked to watch over our Austria.
I congratulate Alexander Van der Bellen on his success and ask all Austrians to stick together and to work together. We are all, equally, Austrians, no matter how we voted at the ballot box.
Rise to Power
One worrying aspect for EU decision-makers was that Hofer's rise to power might also pave the way for a return to government of his popular FPOe, founded by ex-Nazis.
Some 6.4 million Austrians were eligible to vote in Sunday's election.
The official result will only be known once the postal vote has been tallied on Monday.
Back in May, this is what had swung the ballot in favour of ex-Greens party chief Van der Bellen, 72, who beat his rival by just 31,000 votes.
The re-run ends an ugly 11-month campaign which saw Hofer posters being defaced with Hitler moustaches and Van der Bellen's with dog excrement.
"The new president has to unify the country, this long election has polarised society," voter Katharina Gayer told AFP in Vienna.
The far-right candidate had largely avoided inflammatory rhetoric, instead tapping into public anxieties about record immigration and rising unemployment.
His polished style saw him triumph in a first round in April, sensationally knocking out candidates from the two main centrist parties that have dominated Austrian politics since 1945.
The EU hailed Van der Bellen's victory as bolstering European unity at a time of many challenges.
"It is my pleasure to extend my wholehearted congratulations on your election ... On behalf of the European Council and personally, I wish you every success," Council head Donald Tusk said in a statement.
Earlier, European Parliament head Martin Schulz hailed the outcome as a "heavy defeat of nationalism and anti-European, backward-looking populism".
"Congratulations to @vanderbellen who won the presidential election with a clear pro-European message and campaign," Schulz said in a tweet.