Independent candidate Alexander van der Bellen has won Austria's presidential election after far-right leader Norbert Hofer conceded defeat.

The interior minister said on Monday that Alexander Van der Bellen won 50.3 percent of the vote in Sunday's knife-edge election, compared to 49.7 percent for Hofer, presented as the friendly and moderate face of the anti-immigration, populist Freedom Party (FPOe).

"Of course I am sad," Hofer said on Facebook as he conceded defeat. "I would have loved to have looked after this wonderful country for you as president.

"Please don't be disheartened. The effort in this election campaign is not wasted, but is an investment for the future."

Preliminary results late on Sunday had put Hofer 3.8 percentage points ahead in the runoff for the largely ceremonial but bitterly fought-over post of Austrian head of state, but postal ballots, which account for about 12 percent of eligible votes, swayed the result in Van der Bellen's favour.

A record 700,000 postal ballots were counted during Monday, dramatically putting Van der Bellen ahead by just over 31,000 votes in the final tally.