Defeated rival Norbert Hofer, a right-wing populist who is also one of three presidents of parliament, was among those present for the parliamentary ceremony today.
Van der Bellen had narrowly won the initial elections, but Austria's Constitutional Court ordered a repeat after Hofer's Freedom Party claimed widespread voting irregularities.
While the presidency is a mostly symbolic post, the race had attracted Europe-wide attention as the next possible victory for populists after Donald Trump's presidential win in the United States and Britain's Brexit vote.