If Hofer wins, he would become first far-right president in Western Europe since the end of World War II.
Not only are the two from opposite sides of the political spectrum, but it's the second time this presidential election is being run.
It was originally held in May, with former Green Party leader Van der Bellen defeating Hofer by little more than 30,000 votes in a tightly fought contest decided by mail-in ballots.
But the results were annulled over concerns about how some ballots were handled
. So the two candidates, with widely different outlooks, are meeting again in a rerun.
While the Austrian president's role is largely ceremonial, the vote is being closely watched from elsewhere as a yardstick of wider anti-establishment sentiment.
Hofer's party has risen on a populist groundswell sweeping the continent caused by the European Union's failure to make progress in the ongoing economic and migrant crises.
And he may hope his campaign has gained momentum following US President-elect Donald Trump's surprise win last month.
Early in the campaign, Hofer indicated support for a referendum on Austria's membership in the EU, following in Britain's footsteps, but he has since changed his position.
Freedom Party spokesman Karl-Heinz Gruensteidl told CNN that Hofer is not planning a referendum but wants to strengthen Austria's role within the EU, and that he seeks a more federalist EU model.
Van der Bellen, a 72-year-old economist whose parents spent time in a refugee camp before settling in Austria, has championed liberal migration policies.