The results, released shortly after the polls closed, showed Mr Van der Bellen with 53.5 per cent of the vote and Mr Hofer having 46.4 per cent.
While the final result will not be official until absentee votes are counted today, officials said the outstanding vote will not change the outcome, even if the percentages of what the candidates won may vary.
On Facebook last night, Mr Hofer described himself as “infinitely sad” and congratulated Mr Van der Bellen, former head of the Greens, on his victory.
He thanked supporters and described himself as “infinitely sad that it hasn’t worked out”.
He called on all Austrians to work together, “regardless of how we cast our ballots”.
The Austrian president’s functions are largely ceremonial and past elections have merited little attention outside the country because they were decided between mainstream candidates.
This time, though, the contest was different because the vote was seen as an indicator of how well eurosceptic candidates will do elsewhere in the EU next year.
Mr Van der Bellen is pro-European Union and represents liberal to left-of-centre views while Mr Hofer comes from the eurosceptic anti-migrant Freedom Party. Mr Hofer’s campaign message has varied from hard-line when talking to Freedom Party supporters to more moderate when trying to woo undecided voters disenchanted with the political establishment.
Yesterday’s election was a rerun from May, which Mr Van der Bellen won by less than 1 percentage point.
It was re-held following a court ruling after Mr Hofer’s Freedom Party claimed widespread irregularities.
Mr Van der Bellen yesterday noted the outsize attention the election in Austria was receiving.
“What happens here today has relevance for all of Europe,” he said before casting his vote.
Other populist politicians in the EU who want their countries out of the bloc were supportive of Mr Hofer ahead of elections they will face next year. Both far-right National Front leader Marine Le Pen of France and anti-immigrant politician Geert Wilders in the Netherlands tweeted their support.
Mr Hofer opted for a soft tone as he voted. “I want to commit myself to changing this union in a positive way. And I don’t want Austria to leave the European Union, that I have to say very clearly,” he said yesterday in his home village of Pinkafeld, south of Vienna. “(But) our strength is not to be an amorphous entity, our strength is diversity, a diverse European Union.”
His comments reflected his party’s modified message. With most Austrians critical of the EU but not to the point of wanting to leave it, the Freedom Party no longer suggests that Austria would be better off without Brussels. Instead, it is pushing for an EU of loosely allied members mostly sharing economic ties instead of a close political union.
Anton Mahdalik, a Freedom Party member of the Vienna city council, called the result “a great success even though we lost”.
“As a lone party against the Social Democrats, the Popular Party, the Greens, and others, and the establishment media, we still took 2.2 million votes,” he said at the party’s Vienna headquarters shortly after Mr Hofer conceded.
Mr Mahdalik singled out Nigel Farage, the former Ukip leader, for contributing to the party’s defeat after he said on Fox News on Friday that Mr Hofer would hold a referendum on Austria leaving the European Union. “That didn’t help us, it hindered us,” he said, saying that an overwhelming majority of Austrians support EU membership.