Archbishop Christodoulos was a popular public figure in Greece |
The archbishop died on Monday, aged 69, after suffering from cancer.
The funeral, with full state honours, comes after four days of official mourning across the country.
Thousands of people have already paid their last respects to the Archbishop of Athens and all Greece, whose body lied in state at Athens' cathedral.
Aborted surgery
Archbishop Christodoulos was a colourful and controversial figure, says the BBC's Malcolm Brabant in Greece.
He defended the church's pre-eminent role in the state and upheld Hellenism - the national character and culture of Greece, our correspondent says.
But critics said that under Archbishop Christodoulos, Greece remained a country which discriminated against those who were not Orthodox, including Catholics and worshippers of other branches of Christianity.
The archbishop was diagnosed with cancer of the liver and large intestine in 2007.
He was treated in the US for 10 weeks, but a liver transplant operation last October was aborted as the cancer had spread.
He died at his Athens home on Monday morning. Church officials said he had refused hospital treatment in the final weeks of his life.
The Holy Synod, the church's top decision-making body, has now less than 20 days in which to elect the archbishop's successor.
Controversial remarks
Elected as church leader in 1998, Archbishop Christodoulos was known as a fierce and outspoken defender of Greece and the role of the Orthodox Church within it, our correspondent says.
The archbishop once said that when ancient Greeks were creating the lights of civilisation, Europeans were living in trees.
He said Greeks lived in paradise compared to other Europeans because they had a strong faith, built churches, followed traditions and resisted globalisation.
Archbishop Christodoulos opposed Turkey's efforts to join the European Union, describing the Turks as barbarians.
The archbishop clashed with the Greek government when the authorities wanted to remove religious status from identity cards.
"They are trying to take away our society's Christian and Orthodox identity, using various groundless arguments, because they hate God and want to marginalise the Church," he said.