"I entrust you of making proposals for the formation of a new federal government", Van der Bellen told Kurz, as broadcast by ORF.
Kurz, in turn, thanked the president and voters for their trust.
Kurz's OVP secured a landslide victory in the September 29 snap elections. The vote was organised in the wake of a scandal involving the leadership of OVP's coalition partner, the right-wing Freedom Party of Austria (FPO), which led to the resignation of Kurz's previous government.
Back in May, a seven-minute video filmed in 2017 was released showing then-FPO leader Heinz-Christian Strache, who later became vice-chancellor, allegedly discussing exchanging government contracts for help in elections with an alleged niece of a Russian oligarch. The woman was later revealed to be a Bosnian student who was paid for the setup.
The video, which unseated the government, emerged in media just days before the European Parliament elections.
Despite the scandal, OVP won 37.5 percent of the vote. The Social Democratic Party of Austria and FPO won 21.2 percent and 16.2 percent of the vote, respectively.
The Green Party came fourth with a record 13.9 percent.