Greece’s President Prokopis Pavlopoulos named Vassiliki Thanou after efforts to form a coalition failed.
Last week, Alex Tsipras resigned as prime minister to seek a new mandate for office.
Vassiliki Thanou, 65, becomes Greece’s first female prime minister.
Elections are expected to be scheduled for 20 or 27 September.
Vassiliki Thanou’s appointment ends a week of fruitless negotiations as opposition party leaders tried unsuccessfully to form a government.
Alexis Tsipras stepped down as prime minister and called early elections after 25 of his members of parliament quit Syriza over the bailout he agreed with European creditors and formed the left-wing Popular Unity party.
In a statement live on television on August 20, Alexis Tsipras said it was now up to the Greek people to give their verdict on whether to continue with his government’s program.
Alexis Tsipras is expected to win the next election although it is unclear whether he will secure a majority government.
However, he has ruled out a coalition with any of the more centrist opposition parties: centre-right New Democracy, the socialist Pasok party or the small centrist The River (To Potami) party.
Earlier this week an opinion poll for Greece’s Vergina TV suggested support for Alexis Tsipras’s Syriza party had declined to 24%, down from 34% in July.
New Democracy was in second with 22%, while the far-right Golden Dawn ranked third with 6%.
Popular Unity, which split from Syriza, was put on 4.5%.
Panagiotis Lafazanis, who formed Popular Unity, was the last of three party leaders who were given the chance form a government in the past week.
He used the opportunity to air his anti-bailout message before handing back the mandate to the president on Thursday.
Former Finance Minister Yanis Varoufakis decided not to join Popular Unity despite his opposition to the €86 billion ($96 billion) eurozone bailout agreed by his successor Euclid Tsakalotos.
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