President Prokopis Pavlopoulos said he had chosen Vassiliki Thanou, the head of Greece's Supreme Court and the first woman to assume the post.
Mother-of-three Thanou, 65, is known for firing off an emotional letter to European Commission chairman Jean-Claude Juncker in February, protesting that austerity cuts were "annihilating" the Greek people.
"The people are not responsible for the waste of public money by past governments and for mistakes in tax policy," she wrote, adding that the austerity measures "have failed as the recession continues as the rich continue to evade taxes".
The date for Greece's general election is to be officially announced by the end of the week, but it is likely to be scheduled for September 20.
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Outgoing Prime Minister Alexis Tsipras has ruled out forming a national unity government should he fail to win a outright majority in the snap elections triggered after he resigned last week.
Tsipras called for the fresh vote on August 20 after suffering a major rebellion in his hard-left Syriza party over Greece's huge new international bailout, its third in five years.
"I will not become a prime minister who cooperates with New Democracy, Pasok or Potami," Tsipras said in an interview with the Alpha TV channel, his first since resigning.
"If we do not have a majority, I will not cooperate with (the parties that ran) previous governments."
Syriza stormed to election victory in January on a wave of popular anger over tough austerity measures demanded by Greece's creditors in exchange for two previous bailouts since 2010.