Norbert Hofer said he was "very sad that it didn't work out"
The far-right candidate in Austria's presidential election conceded defeat to his independent rival shortly after polls closed on Sunday afternoon.
In a Facebook post, Norbert Hofer said: "I am very sad that it didn't work out. I would have loved to look after our Austria.
"Alexander Van der Bellen I congratulate you for your success and I ask all Austrians to please stick together and let us work together.
"We are all Austrians irrespective of who we voted for. Long live our homeland Austria."
Johannes Huebner, from Mr Hofer's FPO party, confirmed that they had conceded defeat.
Mr Huebner, the party's foreign affairs spokesman, said the numbers showed that Mr Van der Bellen had won, and nothing could change that.
Mr Van der Bellen said his win sends a "message to the capitals of the European Union that one can win elections with high European positions".
After all the ballots cast on Sunday had been counted, Mr Van der Bellen had 51.68% of the vote, compared to 48.32% for Mr Hofer.
But pollsters predicted the split would increase to 53.3% versus 46.7% once approximately 500,000 absentee votes had been tallied up.
The final result is expected by Tuesday at the latest.
Polls prior to the ballot had shown the two candidates neck and neck, meaning the outcome was not necessarily expected.
The election was a re-run of another vote in May, ordered by a court after Mr Van der Bellen won by less than 1%.
Mr Hofer (45) campaigned on promises to close Austria's borders to migrants and to "put Austria first".
Mr Van der Bellen (72) is a retired economics professor who supports the EU, free trade and liberal policies towards migrants.
Previous presidential elections in Austria have attracted little international attention because the post's functions are largely ceremonial.
This time, though, the ballot was seen as an indicator of how other Eurosceptic candidates might do in fellow EU countries next year.
Sigmar Gabriel, Germany's Vice Chancellor, told Bild newspaper: "A load has been taken off the mind of all of Europe."
Mr Gabriel, who heads Germany's centre-left Social Democrats, added the result was "a clear victory for good sense against right-wing populism".
Meanwhile, deputy German justice minister and Social Democrat, Ulrich Kelber, said: "Perhaps (Donald) Trump's election was the turning point.
"The liberal majority pushes back."
The President of the European Parliament, Martin Schulz, said Mr Van der Bellen's win was "a heavy defeat of nationalism and anti-European, backward-looking populism".
French President Francois Hollande said: "The Austrian people made the choice of Europe, and openness."