Tsipraswill assume office at 1700 GMT and told President Prokopis Pavlopoulos that a coalition government with the nationalist Independent Greeks party - his allies in the last Cabinet - would be sworn in by Wednesday morning.

Later on Wednesday the PM will travel to Brussels for a summit on the refugee crisis where he will also represent Cyprus.

Over 310000 migrants and refugees have landed on Greek shores from Turkey this year most of them Syrians fleeing their country's civil war.

France Germany Spain and European Council president Jean-Claude Juncker pledged to help Greece through both on the economic front and in dealing with the worsening migrant crisis.

The new government will be tasked with enforcing a rescue package worth up to US$97bn.

EU partners wasted no time in reminding Greece to get down to work on the reforms.

"Looking forward to swift formation of new government with strong mandate to continue reform process" said Eurogroup president and Dutch Finance Minister Jeroen Dijsselbloem.

From buying a loaf of bread to a visit to the doctor pain lies in store as the new government readies to raise taxes and rewrite the economic rule-book in line with tough reforms demanded by the country's lenders in return for Greece's third international rescue in five years.

"There's a lot of work ahead and no time to lose" said Juncker. "As you know well you can count on the European Commission and on me personally to stand by Greece and support the new government in its efforts."

Commission spokesman Margaritis Schinas said Greece's creditors -- the EU the European Central Bank and the International Monetary Fund -- would meet over the next few months to conduct a review aimed at releasing new funds under the bailout deal.

The economic to-do list was signed in July by Tsipras in a controversial deal that alienated anti-euro hardliners who then quit his Syriza party stripping the premier of his majority and triggering Sunday's general election.

With all votes counted in the September 20 ballot Syriza secured 35.46 per cent of the vote close to an absolute majority of 145 seats in the country's 300-seat parliament. Coalition partner ANEL can provide another ten lawmakers.

"Syriza proved too tough to die" Tsipras at 41 the country's youngest Prime Minister in 150 years and the EU's first radical left leader in office told a victory rally in Athens on Sunday evening.

Tsipras who had justified the deal he signed in July with European leaders as saving Greece from a chaotic exit from the eurozone said the election victory would 'change the balance' in Europe and strengthen Greece's fight against endemic corruption and hidden wealth.

Syriza's main rivals the conservative New Democracy Party came second on 28.10 per cent while Syriza defectors who had formed a rival anti-austerity party failed to pick up the required three percent of the vote to enter parliament.

In an indication of Greece's weariness with five years of economic crisis and political tumult nearly 44 per cent of voters sat out the election - the third vote for Greeks this year including a referendum on austerity. The abstention rate during the January election stood at 36 per cent.

Post-victory celebrations also indicated crisis fatigue with only around 500 jubilant Syriza supporters turning out to congratulate Tsipras on a hot Athens night against 8000 in January.

Greece's new parliament expected to convene on October 1 will have to revise the 2015 budget taking into account pension and income tax reforms including taxes on farmers' income that are set to double by 2017.

The government must also finalise a procedure to recapitalise Greek banks by December before new EU-wide bank rescue regulations that could affect depositors come into play in 2016.

Tsipras must also move quickly to remove capital controls that his previous administration imposed in June to avert a deposit run.

A total of eight parties booked seats in the next parliament with neo-Nazi party Golden Dawn in third place followed by the Pasok socialists.