Greens-backed independent Alexander Van der Bellen, 72, swept 53.6 per cent of the votes, while his rival of the anti-immigration Freedom Party (FPOe) received 46.4 per cent, projections showed.
The official result of the marathon presidential election, which lasted nearly a year, is not expected before tomorrow, but the party conceded defeat within minutes of the poll projections being released, shortly after voting ended.
"I would like to take this opportunity to congratulate Mr Van der Bellen," FPOe chief strategist Herbert Kickl told Austrian media.
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.
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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 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.
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.
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 today's election.
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.
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