Immediately after sweeping to victory on Sunday, Van der Bellen pledged to project a pro-European stance to the world.
After he saw off a challenge by a candidate from the far-right Freedom Party, Van der Bellen said Austria had sent "a signal of hope and positive change throughout Europe."
In a statement, Van der Bellen, 72, said, "It's a signal that will be taken in and carefully analysed in the EU's capitals.
He added, "You can actually win elections with a pro-European position."
Europe had braced for what could have been the election of the continent's first far-right President since World War II, but it was the centre-left contender who won. Vote projections showed Van der Bellen ahead of far-right rival Norbert Hofer, 53.6 per cent to 46.4 per cent.
Van der Bellen, who stood as an independent candidate but was backed by the Green Party, had won an earlier round that was later declared invalid because of irregularities, prompting a second election.
Hofer had previously demanded a referendum on Austria's EU membership, comparable to the Brexit vote in the UK.
Hofer said, "I am very sad that it didn't work out. I would have loved to look after our Austria. Alexander Van der Bellen, I congratulate you for your success and I ask all Austrians to please stick together and let us work together."
Reaction from the EU side was swift, with European Parliament President Martin Schulz saying Van der Bellen's victory was "a heavy defeat of nationalism and anti-European, backward-looking populism."
European Council President Donald Tusk offered his "wholehearted congratulations" and wished Van der Bellen "every success."
Tusk said, "At a time when we are faced with many difficult challenges, the continued constructive contribution of Austria to finding common European solutions and keeping our European unity will remain essential."
More comment came from European Green party Co-Chairs Reinhard Bütikofer and Monica Frassoni who said, "It's a truly historical day for Austria and Europe.
"Austrians chose a President who is not polarising against others but who will work to create real, positive transformation for the country and EU as a whole.
"Van der Bellen has a long, remarkable political experience and his election gives hope for the future of Europe. The impressive support his campaign received from across Europe shows how a big share of Europeans really doesn't buy the nationalistic and populistic narrative.
"Let's build on this momentum and carry this vibe with an eye to the next challenges to be faced in 2017."
French President François Hollande tweeted, "The Austrian people have chosen Europe", while Germany's foreign Minister Frank-Walter Steinmeier said, "All of Europe is relieved."
Thomas Strobl, a deputy Chair of German Chancellor Angela Merkel's Christian Democratic Union party, said, "It's an encouraging sign that the power of common sense can defeat hate, anger, nationalism and lies in our democracies."
Both France and Germany are paying particularly close attention as they, along with the Dutch, face their own elections next year.
French far-right politician Marine Le Pen responded to Hofer's loss with a tweet congratulating his Freedom Party for fighting "with courage."
"They'll be victorious in the next legislative elections", she added.
GUE/NGL group leader Gabi Zimmer said, "It is good to see many more people voted for him this time than for Hofer.
"Nevertheless, this election should be seen as a warning instead of being a watershed moment against the far right such as Strache, Le Pen and Wilders. This is because the underlying reasons which give rise to the far right are still there.
"Inequality and the growing rich-poor divide, job insecurity and unemployment continue to strike fear among more and more EU citizens. The far right will continue to unscrupulously exploit these conditions for their own gain," added the German MEP.
"As long as the EU continues with its austerity policies and is not willing to offer an alternative that benefits ordinary people instead of multinationals and banks, more people will choose the far right as the alternative to EU's current neoliberal model."