In a statement posted on his Facebook page Hofer thanked his supporters and said he was infinitely sad that it did not work out.
He added that Van der Bellen had expressed to him his desire for Austria to unite and work together going forward.
The news comes as fears grew among Europe that the country was about to elect the continents first far-right leader since the Second World War.
Sigmar Gabriel, vice chancellor of the centre-left Social Democrats told Bild newspaper: A load has been taken off the mind of all of Europe. This is a clear victory for good sense against right-wing populism.
Van der Bellen, who is backed by the Green Party, was said to be leading the vote with 53.6% as the polling stations closed on Sunday at 5pm, local time (4pm GMT).
Ahead of the polls closing in Sunday, many had said the result was too close to call.
Many predicted that the result of the election would be influenced by perceived victories for the right in the UKs EU referendum and Donald Trump in the US Presidential election earlier this month. With key elections taking place next year in the Netherlands and France, this will be seen as an indication of the likely outcomes.
Hofer, a member of the far-right Freedom Party, has been the subject of protests in Austria over the weekend as his colleagues have some forward to defend the party against allegations of Nazism. The 45-year-old campaigned on an anti-immigration platform as concerns in the country have grown over an influx of refugees attempting to access Germany.
The Freedom Party was established in the 1950s by Nazi sympathisers. The pan-Germany party sits in the European Parliaments Europe of Nations and Freedom (ENF) group. The ENF group is attended by members of far-right French political Party Front National, and chaired by candidate in the 2017 French Presidential election, Marine le Pen.
