The announcement marks a dramatic reversal for the president, a former leader of the Greens who has long been critical of the Freedom Party (FPO) and has clashed with its leader Herbert Kickl, but few options remained to van der Bellen after the centrists' failure to forge a coalition.
The anti-immigration and European Union-sceptic Freedom Party, which opposes sanctions against Russia, won Austria's parliamentary election in September.
It took 28.8 per cent of the vote and beat outgoing Chancellor Karl Nehammer's conservative Austrian People's Party (OVP) into second place.
But in October, van der Bellen gave Nehammer the first chance to form a new government after Nehammer's party said it would not go into government with the FPO under Kickl and others refused to work with the Freedom Party at all.
Those efforts to form a governing alliance without the FPO collapsed in the first few days of the new year and Nehammer said on Saturday that he would resign.
The People's Party then signalled that it might be open to working under Kickl.
Van der Bellen said after meeting Kickl for about an hour at the presidential palace on Monday that he had tasked the Freedom Party leader with holding talks with the People's Party to form a new government.
During the conversation, Kickl assured him that he was confident of being able to fulfil the role of chancellor, van der Bellen said.
"Respect for the electorate's vote requires that the president respect the majority," even if he himself might have other wishes and ideas, van der Bellen said.
"I did not take this step lightly," the president told reporters.
"I will continue to take care that the principles and rules of our constitution are correctly respected and adhered to."
As Kickl left his meeting with the president, hundreds of protesters including Jewish students and progressive activists booed, whistled, chanted "Nazis out" and waved banners with slogans such as "We don't want a right-wing extremist Austria".
Van der Bellen had infuriated the FPO by not tasking it with forming a government soon after the election since no potential coalition partner was immediately forthcoming.
Nehammer had long insisted his party would not govern with Kickl, saying the FPO leader was a conspiracy theorist and security threat.
With Nehammer gone, so is that red line.
His interim successor as OVP leader, Christian Stocker, said on Sunday his party would join coalition talks led by Kickl.
"We are at the very beginning. If we are invited to these talks, the outcome of those talks is open," OVP heavyweight Wilfried Haslauer, the governor of Salzburg state who stood next to Stocker at his first statement to the media as designated party leader, told broadcaster ORF.
Should those talks fail, however, a snap election is likely and opinion polls show FPO support has only grown since September.
The OVP and FPO overlap on various issues, particularly over taking a tough line on immigration.
The OVP and the FPO had already formed coalitions in the 2000s and between 2017 and 2019 - albeit with the OVP always holding the top role of chancellor.
with AP and DPA
