With most districts counted, Prime Minister Alexis Tsipras admitted defeat to his rival, Kyriakos Mitsotakis, the BBC reported on Monday.
New Democracy has 39.8 per cent of the vote so far, with Tsipras's leftist Syriza party in second place with 31.6 per cent.
Current projections give New Democracy an outright majority, as the winner receives 50 extra seats in parliament.
So far, about 88 per cent of districts have returned their results.
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 president for all because Greeks were "too few to stay divided".
Speaking as the results became clear, Tsipras confirmed he had called 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," Tsipras told journalists.
Turnout in the election was about 57 per cent one of the lowest figures in decades.
Voting is technically compulsory in the country, though the rule is not enforced.
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 35 degrees Celsius in places.
( With inputs from IANS )