With 91 per cent of votes counted, New Democracy was leading with 40.5 per cent of the vote and 158 seats in the 300-seat parliament, interior ministry figures showed.
It was more than 20 points clear of Syriza, a radical progressive party which won elections in 2015 at the peak of a debilitating debt crisis and which ran the country until 2019, when it lost to New Democracy.
"This freely given support only increases my reponsibility to respond to people's hopes. I personally feel an even stronger obligation to serve the country with all my abilities," Mitsotakis told cheering crowds at New Democracy headquarters in downtown Athens.
Mitsotakis, 55, a former banker and scion of a powerful political family, has promised to boost revenue from the vital tourist industry, create jobs and increase wages to near the European Union average.
He came to power in 2019, ousting the radical Syriza party, at the peak of a debilitating debt crisis which almost resulted inGreece toppling out of the euro zone.
"Obviously this is a great defeat," Euclid Tsakalotos, who was finance minister under the Syriza administration, told Greece's Skai TV.
Based on early projections, Syriza had 47 seats in parliament - a resounding defeat for the party.
Mitsotakis, who was prime minister from 2019 until stepping down in favour of a caretaker prime minister following an inconclusive May vote, has vowed to push ahead with reforms to rebuild the country's credit rating after the debt crisis which wracked Greece for a decade.
Sunday's vote was the second in the past five weeks, as a first poll on May 21, held under a different electoral system, failed to give a single party absolute majority in parliament.
The system used in Sunday's poll gives the leading party bonus seats depending on voter support.
The COVID-19 pandemic and a deadly rail crash in February exposed shortcomings in Greece's health and public transport systems.
But a cost of living crisis and economic hardship have more recently topped voters' concerns.
"I expect a lot (from the new government)," pensioner Giorgos Katzimertzis told Reuters.
"The main thing is the health system, the economy, so we can live (decently) because things are difficult. I am a pensioner, I was on the fire brigade, and now I don't have a dime."
Sunday's election was held in the shadow of a migrant shipwreck this month in which hundreds are feared to have perished off southern Greece.
One of the worst such disasters in years, it has exposed the parties' divisions over migration.
An anti-immigrant party, the Spartans, which said Greece was threatened by uncontrolled migration, was the surprise of the campaign.
It was set to gain 4.7 per cent of the vote and up to 13 seats in parliament, based on the early results.
The group was catapulted from relative obscurity after support from Ilias Kasiadiaris, the frontman of the now-banned Golden Dawn ultranationalist party.
His own party was barred from the elections and he endorsed the Spartans from jail.
The shipwreck disaster dominated campaigning in the run-up to this election.
Rescuers found 104 survivors and recovered 82 bodies but up to 750 people are thought to have been packed on the ramshackle vessel heading from Libya to Italy.
The boat had been shadowed by the Greek coast guard, which said occupants refused all offers of help.
Mitsotakis, whose administration has taken a tough line on migration, has blamed "wretched traffickers" for the disaster and praised the coast guard for rescuing people.
Tsipras has questioned why the coast guard did not intervene earlier.
