Leader of Greece's leftist SYRIZA party Alexis Tsipras has spoken to a cheering multitude in Athens following results of exit polls which give him a clear victory over ruling New Democracy.

"Today the Greek people wrote history... the Greek people gave a powerful mandate. Greece is changing the page," the 40-year-old leader, who wants to reverse the austerity program his country is undergoing has told the crowd.

He has also called the Troika of international lenders - the European Union, the European Central Bank (ECB) and the International Monetary Fund (IMF) - "a thing of the past".

"Today, friends, citizens of Athens, I address every Greek man and woman. There are no victors or vanquished. Today we defeated the oligarchy. If someone won today, it is Greece, in order to create a new future with dignity," the BBC quotes Tsipras as saying.

He has also made a reference to other EU member states that have suffered from the economic and financial crisis and subsequent austerity measures by arguing his victory "is of all the peoples of Europe who are struggling" and has voiced his party's readiness to seek a solution which would return Europe to "development and social stability and values like democracy and solidarity."