The last election result from May was annulled after Austria's highest court in July upheld the narrowly defeated far-right's claims of procedural irregularities.
And in a fresh twist, the government was on Monday forced to postpone October's planned re-run after it emerged that the envelopes for postal votes were not sticky enough, meaning they could easily be reopened.
In the May election, Norbert Hofer of the far-right Freedom Party (FPÖ) narrowly lost by just 31,000 votes to independent ecologist Alexander Van der Bellen.
If he wins this time, Hofer would become Europe's first far-right head of state since 1945.
Voting by post is popular in Austria, and was used by some 17 percent of voters in May.
Both the centre-left SPOe and their centre-right coalition partners the People's Party (ÖVP) signed a bill proposing the new vote on December 4, along with the opposition Greens and NEOS.
This wide backing should ensure the bill passes easily with the two-thirds majority needed.
But the far-right said it would not back the bill, demanding heavy limits on postal voting, which it traditionally opposes.
Austria has been without a president since July 8 when Heinz Fischer stepped down. He was replaced on an interim basis by the speaker of parliament and two deputy speakers.
The role of Austria's president is largely ceremonial but not entirely. He or she can in theory sack the government — something that Hofer has in the past threatened he would do.