Greece's parliament on Wednesday elected the first woman president in the country's history, a senior judge with no party-political allegiance.

A cross-party majority of 261 of the 294 MPs present at the session voted in favour of 63-year-old Ekaterini Sakellaropoulou, parliament chief Costas Tassoulas said.

"Ekaterini Sakellaropoulou has been elected president of the republic," Tassoulas said.

"This is a very important day for the Greek republic," said Prime Minister Kyriakos Mitsotakis, who nominated her for the post.

"Parliament has elected a remarkable jurist, a consensus figure who symbolises the transition to a new era."

The new EU Commission President Ursula von der Leyen agreed. Tweeting her congratulations to Sakellaropoulou, she added: "Greece is moving ahead into a new era of equality."

Sakellaropoulou herself set out her priorities to assembled journalists shortly after the vote: the economic crisis, climate change and mass migration, all of which required international cooperation.

The new president, until now the head of Greece's administrative court, the Council of State, will be sworn in on March 13, taking over from Prokopis Pavlopoulos.

The daughter of a Supreme Court judge, Sakellaropoulou completed postgraduate studies at Paris's Sorbonne university. She was the first woman to lead the Council of State, the country's top administrative court.

As a jurist, she has particular expertise in environmental and constitutional law.

Although the president is nominally the head of the Greek state and commander-in-chief, the post is largely ceremonial.