The vote pits 45-year-old Norbert Hofer of the anti-immigration Freedom Party (FPOe) against the Green-backed economics professor Alexander van der Bellen, 72.
A year of rising concerns about the migrant crisis and growing unemployment has left Austria deeply polarised and driven disgruntled voters away from traditional parties toward fringe groups.
In last month's first round, Hofer -- a gun enthusiast left partially disabled after a paragliding accident -- comfortably beat his rival by 35 per cent to 21 per cent.
"I will be your new president, a patron for Austria," he told a jubilant crowd at the Viktor-Adler square in Vienna's Favoriten district, an FPOe stronghold.
Hofer's win would also pave the way for the FPOe to head the next government after parliamentary elections, scheduled for 2018.
Polling stations opened at 0500 GMT and the first results are expected at 1500 GMT. Final results will be announced tomorrow after postal votes have been counted.
They could prove to be a tie-breaker in the race, with close to 900,000 people -- or a record 14 per cent of Austria's 6.4 million eligible voters -- casting their ballot by mail this year.
Described as the FPOe's "friendly face", Hofer has pushed populist themes with a winning smile instead of the inflammatory rhetoric used by party leader Heinz-Christian Strache.
The approach paid off, earning the FPOe its best result at federal level last month.
Meanwhile voters punished the two main parties, which were knocked out of the race with just 11 per cent.
The crushing defeat means that for the first time since 1945, the president will not come from the Social Democrats (SPOe) or centre-right People's Party (OeVP).
European leaders including European Commission chief Jean-Claude Juncker have voiced concern at the turn of events in Austria.
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