According to MetronAnalysis' pollster Fanaras Syriza will come just one seat short of winning a parliamentary majority with 150 seats.
The anti-austerity party has promised to reverse massive spending cuts and negotiate a write-off of Greece's debts. Tsipras's principal opponent is the conservative New Democracy party, which make-up the current government. The exit polls showed New Democracy taking 23-27 per cent of the vote.
New Democracy has pushed ahead with economic reforms recommended by the Troika - the European Union (EU), International Monetary Fund (IMF) and European Central Bank (ECB). While the deficit has been eliminated and growth has returned many Greeks are still immensely poorer than they were five years ago.
The Greek parliament is comprised of 300 members. The party that wins the largest share of the vote is awarded an additional 50 MPs. After voting this morning, Tsipras said, "the vicious circle of austerity is over".
Syriza's programme of debt relief and an end to austerity have set the party on a collision course with other EU member states. Angela Merkel, in particular, will be unwilling to give way to Tsipras's demands for fear of a backlash at home and encouraging radical parties in other member states. Syriza has attempted to moderate its positions over the course of the campaign, saying it wants Greece to remain in the Euro.
A Syriza victory followed by political deadlock could lead to Greece defaulting on its debts and exiting the Euro. Last week, ratings agency Moody's has warned that the heightened risk of a Greek exit from the Eurozone "could have negative credit implications for other members of the European single currency".
However, the Eurozone is in a far better shape to withstand any contagion from a Grexit than it was five years ago. But a Grexit would still be a seminal moment for the currency block, said chief credit officer, Colin Ellis:
Any exit from the single currency would be a defining moment for the euro: it would show that the monetary union is divisible, not irreversible.