In the end there was just a 0.6 percent difference, with Van der Bellen receiving 50.3 percent and Freedom Party's Norbert Hofer receiving 49.7 percent.
Posting on social media, Hofer has also admitted defeat to his Green-backed opponent, thanking people for their support.
The win from van der Bellen means Austria did not become the first country in the EU to have a head of state from the anti-immigrant far-right.
Projected results late on Sunday put both Hofer, presented as the friendly and moderate face of the populist Freedom Party (FPÖ), and Alexander van der Bellen, former head of the Greens, neck-and-neck on 50 percent.
In the end it came down to some 750,000 valid postal votes which were counted on Monday and added to the total. Early reports suggest it came down to just a matter of a thousand votes in the end.
In the first round on April 24th, the candidates of the Social Democrats (SPÖ) and their centre-right coalition partners People's Party (ÖVP), came a disastrous fourth and fifth with just 11 percent of the vote.
That meant that for the first time since 1945, these parties, which have long dominated politics in one of the EU's most stable democracies, had to watch the second round from the sidelines.
This was also the final straw for Werner Faymann of the SPÖ, who quit as chancellor on May 9th.
Already on Tuesday, members of the losing FPÖ were alleging cases of electoral fraud.
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