The country has its general elections next month, and the Panhellenic Socialist Movement, known as Pasok, is seen as reviving one of the country's political dynasties as it fights to retain power, the Times of London said.
More than a million Pasok supporters joined 146,000 registered party members at more than 2,500 polling booths Sunday to vote for their new leader.
Papandreou was mobbed by hundreds of supporters chanting "You are and you will be prime minister" as he arrived at an Athens polling station.
Friday, at the Pasok party congress, Papandreou, currently the foreign minister, was the only nominee to lead the party into the election.
Costas Simitis, the former leader and a two-term prime minister, voted for Papandreou after announcing last month that he would step down in favor of Papandreou the day after the election.
Papandreou's late father, Andreas, founded Pasok and was renowned for his anti-U.S. rhetoric.
Celebrity Families of 2014 [PHOTOS]