The election gives Norbert Hofer, 45, of the opposition Freedom Party (FPOe) another shot at becoming the European Union's first far-right anti-immigration president.
Hofer lost out to Alexander Van der Bellen, a 72-year-old Greens-backed independent, by just 31,000 votes in May.
The FPOe launched a legal challenge on June 8 alleging "terrifying" irregularities, and on July 1 Austria's highest court upheld its challenge, ruling that Austrians must vote again.
The Constitutional Court found that procedural errors took place with almost 80,000 votes, meaning that they potentially could have been tampered with.
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Traditionally the president's job has been largely ceremonial but Hofer has indicated that he would make use of hitherto untapped powers afforded under Austria's constitution.
Winning the Hofburg palace would also be of enormous symbolic importance for the FPOe two years before the next scheduled general elections, and be a fillip to other populist parties across Europe.
Experts say it is impossible to predict the election outcome, although some say that they expect a lower turnout, which could boost Hofer, who says Islam has no place in Austria.
Economics professor Van der Bellen, 72, is staunchly pro-EU, and surveys have shown a clear majority of Austrians in favour remaining in the bloc.