Syriza has pledged to reject austerity and cancel the country's billions of euros in debt. The party's victory is a resounding rebuff to the country's loss of financial sovereignty.
With 92 per cent of the vote counted, Greeks gave Syriza 36.3 per cent of the vote - 8.5 points more than conservative New Democracy party of Prime Minister Antonis Samaras. It means they will be able to send between 149 and 151 MPs to the 300-seat Parliament, putting them close to a majority. The final result was too close to call.
Syriza is now likely to become the first anti-austerity party in Europe to form a government. Samaras gave a brief statement in which he accepted the result and claimed he had put Greece back on the road to recovery.
Tsipras, 40, an admirer of Che Guevara, is expected to be Greece's youngest prime minister in 150 years. The party wants to roll back five years of austerity policies and cancel a large part of Greece's 318 billion ($480 billion) debt. If they fulfil the threats, Greece's membership of the euro zone could be in peril. Tsipras has toned down the anti-euro rhetoric he used during Greece's last election in 2012 and now insists he wants Greece to stay in the eurozone.
Austerity policies imposed by the EU and IMF have produced deep suffering, with the economy contracting by a quarter, youth unemployment rising to 50 per cent and 200,000 Greeks leaving. Tsipras has pledged to reverse many of the reforms that the hated "troika" of the EU, IMF and European Central Bank have imposed, including privatisations of state assets, cuts to pensions and a reduction of the minimum wage.