President Prokopis Pavlopoulos named Ms Thanou after efforts to form a coalition failed. Last week, Alex Tsipras resigned as prime minister to seek a new mandate for office.
Ms Thanou, 65, becomes Greece’s first female prime minister.
Elections are expected to be scheduled for 20 or 27 September.
Ms Thanou’s appointment ends a week of fruitless negotiations as opposition party leaders tried unsuccessfully to form a government.
Mr Tsipras stepped down as PM and called early elections after 25 of his MPs quit Syriza over the bailout he agreed with European creditors and formed the left-wing Popular Unity party.
In a statement live on television last Thursday, he said it was now up to the Greek people to give their verdict on whether to continue with his government’s programme.
Mr Tsipras is expected to win the next election although it is unclear whether he will secure a majority government.
