Austria's far-right anti-immigration party concedes defeat in presidential race
Greens-backed independent Alexander Van der Bellen, 72, swept 53.6 percent of the votes, while rival Hofer received 46.4 percent, projections showed.
The official result of the marathon presidential election - which lasted nearly a year - is not expected before Monday, but the party conceded defeat within minutes of the poll projections being released, shortly after voting ended.
"I would like to take this opportunity to congratulate Mr Van der Bellen," Freedom Party chief strategist Herbert Kickl told Austrian media.
During Hofer's campaign, the far-right candidate tapped into public anxieties over an immigration hike following the arrival of some 130,000 migrants to Austria in the past two years.
"The new president has to unify the country, this long election has polarised society," voter Katharina Gayer told AFP in Vienna.
While commentators predicted a far-right victory in Austria's election on the wave of Donald Trump's shock election in the US and UK's unexpected vote to quit the EU, electorates in Austria bucked the trend of right-wing populism in Europe.
A populist tide has been sweeping the continent as Europe battles its worst migration crisis since the Second World War, struggling to cope with the arrival last year of hundreds of thousands of refugees and other migrants from the Middle East, Africa and South Asia.
Some 6.4 million Austrians were eligible to vote in Sunday's election.
The official result will only be known once the postal vote has been tallied on Monday.