Kyriakos Mitsotakis leaves the presidental palace flanked by his children after being sworn-in as a prime minister on Monday. Louisa Gouliamaki / AFP

After a sweeping election victory Greece's conservative leader Kyriakos Mitsotakis was sworn in as new prime minister on Monday.

The victory put him in charge of the EU's most indebted member with promises to end a decade of economic crisis.

"The Greek people gave us a strong mandate to change Greece. We will honour it to the full," Mitsotakis said after taking his oath of office in a televised ceremony.

"Hard work begins today. I am completely confident that we will prove equal to the challenge." The cabinet will be sworn in on Tuesday and will meet on Wednesday, he said.

The 51-year-old Harvard graduate and former McKinsey consultant took the oath of office in the presidential mansion in the presence of his wife and three children.

He then walked next door to the prime minister's office, where he had a brief discussion with defeated leftist premier Alexis Tsipras.

The US-educated conservative faces a hefty challenge as he takes over from Tsipras, who imposed austerity measures required under a bailout to keep Greece in the eurozone.

The country's public debt last year stood at 335 billion euros ($376 billion), or 180 per cent of GDP.

The debt load is forecast to fall to 168 per cent of GDP this year, but only under belt-tightening brought in under Tsipras's Syriza party − something that Mitsotakis's New Democracy party says is stifling growth.

The tricky job of keeping Greece's international creditors onside while easing the hardship on Greeks − by lowering taxes and renegotiating fiscal targets − could result in a short honeymoon phase for Mitsotakis.

A Eurogroup finance meeting on Monday will convene to discuss the state of Greece's economy after tax cuts rolled out by Tsipras in a last-ditch attempt to win over voters May.

The former banker has pledged to create jobs and "steamroller" obstacles to business.

Those pledges wooed Greek voters, who handed him 40 per cent of the votes in Sunday's election, well ahead of the 31.5 per cent given to Tsipras.

"It's a strong message for change in Greece," Mitsotakis told reporters on Sunday.

Last week he told reporters that he saw it as his mission "to make sure we restart the economy" with "ambitious growth driven by private investments, exports and innovation".

He predicted that he could persuade Greece's creditors to accept the easing of tight fiscal targets if "a comprehensive reforms package" was presented.

Tsipras, for his part, warned that Mitsotakis would do away with the social spending he brought in to help Greece's vulnerable groups.

He portrayed the Mitsotakis family − one of Greece's leading political dynasties − as part of a failed system that bankrupted the country in 2010, which he blamed for the humiliating bailout.

Mitsotakis is the son of former prime minister Constantine Mitsotakis, one of the country's longest-serving parliamentarians.

His sister Dora Bakoyannis is a former minister and Athens's first female mayor.

And in a first even for a country accustomed to family links in politics, the new mayor of Athens is the incoming PM's nephew.

Mitsotakis took charge of the New Democrats three years ago. Following the election, his party will have a majority of 158 seats in the 300-member parliament.

New Democracy was last in power in 2014, in coalition with the Greek socialists.

Syriza's parliamentary presence will shrink from 144 seats to 86. Tsipras has promised to remain an "active" voice in opposition.

Sunday's election was Greece's third in as many months.

In May, New Democracy beat Syriza by nearly 9.5 points in European parliament elections. A week later, it completed a near-sweep of Greek regions in local elections. After that, Tsipras was forced to call an early general election.

"A painful cycle has closed," Mitsotakis said in a televised address immediately following his electoral victory, adding that Greece would "proudly raise its head again" on his watch.

Entering parliament for the first time are Greek Solution, a nationalist party formed by TV salesman Kyriakos Velopoulos, and MeRA25, an anti-austerity party founded by maverick economist and former Greek finance minister Yanis Varoufakis.

Neo-Nazi party Golden Dawn was shut out of parliament for the first time since 2012.

Golden Dawn, until recently Greece's third-ranking party, is in steep decline amid an ongoing trial for the 2013 murder of an anti-fascist rapper, allegedly carried out with the knowledge of senior Golden Dawn members.
Agence France-Presse