The conservative New Democracy party of Kyriakos Mitsotakis had 39.7% of the vote compared to Tsipras' Syriza party with 31.5% after nearly 60% of ballots were tallied.
"The citizens have made their choice. We fully respect the popular vote," Tsipras said in his concession speech from central Athens, adding that he had phoned Mitsotakis to congratulate him.
"I want to assure the Greek people that ... we will protect the rights of working people with a responsible but dynamic opposition," he said.
"I wish and hope that the return of New Democracy to government will not lead to vengeance ... particularly toward the significant achievements to protect the social majority and the workers," Tsipras continued.
Official projections based on early partial results also showed the extreme right-wing Golden Dawn party teetering on the lower side of the 3% threshold needed to be in parliament. Golden Dan became the third-largest party in parliament during Greece's financial crisis,
Greece is gradually emerging from the crippling financial crisis that saw unemployment and poverty levels skyrocket and the economy shrink by a quarter.
Greece was dependent for survival until last summer on three successive bailouts and had to take deep reforms such as massive spending cuts and tax hikes to qualify for the rescue loans.
Tsipras, 44, called the election three months ahead of schedule after his left-wing Syriza party suffered a severe defeat in European Union and local elections in May and early June.
To gain ground, he increasingly appealed to a middle class struggling under a heavy tax burden, much of it imposed by his government.
Tsipras led his small Coalition of the Radical Left, or Syriza, party to power in 2015 on promises to repeal the austerity measures of Greece's first two bailouts.
But after months of tumultuous negotiations with international creditors that saw Greece nearly crash out of the European Union's joint currency, he was forced to change tack, signing up to a third bailout and imposing the accompanying spending cuts and tax hikes.
He also cemented a deal with neighboring North Macedonia under which that country changed its name from plain "Macedonia." Although praised by Western allies, the deal angered many Greeks, who consider use of the term harbors expansionist aims on the Greek province of the same name.
Mitsotakis, 51, the son of a former prime minister, brother of a former foreign minister and uncle to a newly elected mayor of Athens, had been ahead in opinion polls for three years and managed to build a sizeable lead.
He fought to shed the image of family privilege and had pledged to make Greece more business-friendly, attract foreign investment, to modernize the country's notorious bureaucracy and to cut taxes.
"Today, voters take the decision for their future in their hands," Mitsotakis said after voting. "I am sure that tomorrow, a better day dawns for our nation."
Official projections based on early partial results showed six parties entering parliament, with New Democracy holding 158 of the body's 300 seats, a comfortable governing majority.
Golden Dawn was hovering at around 2.96%, said Yiannis Theodoropoulos of SingularLogic, the company compiling the official election results for the Interior Ministry. If it manages to push above the 3% threshold to enter parliament, that would reduce New Democracy's number of seats from the 158 it was projected to have.
Demetris Nellas and Stefania Vourazeri in Athens contributed.
Full coverage at https://www.apnews.com/Greece