Turnout in the election was about 57% – one of the lowest figures in decades.
There have been a half dozen elections in recent years and on Sunday, many residents flocked to the beaches or sheltered at home as temperatures exceeded 35C in places.
What did Mitsotakis say in his victory speech?
The prime minister-elect told supporters he had been given a strong mandate for change.
“The country proudly raises its head again,” he told the crowd in the capital Athens, saying he would be a prime minister for all because Greeks were “too few to stay divided”.
Speaking as the results became clear, Mr Tsipras confirmed he had called Mr Mitsotakis to offer him his congratulations.
“Today, with our head held high we accept the people’s verdict. To bring Greece to where it is today we had to take difficult decisions [with] a heavy political cost,” Mr Tsipras told journalists.
Outgoing European Commission President Jean-Claude Juncker congratulated Mr Mitsotakis on his “clear victory”.
What does New Democracy stand for?
New Democracy has promised to lower taxes and privatise services in the country, which is still feeling the effects of the 2008 financial crisis.
Greece has been in receipt of a series of bailout programmes over the past decade, which it officially “exited” last August as economic growth returned.
But youth unemployment remains high, and New Democracy has counted many 18-24 year olds among its supporters.
The potential new prime minister comes from one of Greece’s long-standing political dynasties.
Kyriakos Mitsotakis is the son of former Prime Minister Konstantinos Mitsotakis. His sister, Dora Bakoyannis, was mayor of Athens when the city hosted the Olympics in 2004, before becoming Greek foreign minister.