Pikramenos, head of one of Greece's three highest courts, received the mandate Wednesday to form the new government, state television reported.
He called the role "a great burden" but thanked President Karolos Papoulias for putting his trust in him. Pikramenos, whose name means "embittered," said he had perhaps the most appropriate name for the job, ekathimerini.com reported.
Papoulias said the likeliest date for a second round of elections was June 17.
The New York Times said the eurozone is concerned about the upcoming elections, fearing anti-bailout sentiment in Greece's Parliament could lead the nation to default on its debts.
Papoulias said Tuesday nearly $900 million had been pulled from Greek banks on Monday and the Greek central bank warned of the potential for a panic.