Official results with more than half of ballots counted showed Mitsotakis' New Democracy party comfortably winning Sunday's election, receiving 39.7% of the vote compared to 31.5% by Tsipras' Syriza party.
The election is likely to give Mitsotakis a comfortable parliamentary majority.
In a speech from central Athens on Sunday night, Tsipras said: "The citizens have made their choice. We fully respect the popular vote."
The projections from Sunday's election also had the extreme right-wing Golden Dawn teetering on the lower side of the 3% threshold needed to enter parliament.
Yiannis Theodoropoulos of SingularLogic, the company compiling official election results for the Greek Interior Ministry, said the projections show New Democracy holding 158 of the 300 seats in Greece's parliament, a comfortable governing majority.
Support for Golden Dawn hovered at around 2.96%. If the party manages to hit the minimum threshold and become the seventh party in parliament, it would reduce the number of seats held by New Democracy members.
Greek Finance Minister Euclid Tsakalotos says the conservative opposition New Democracy party won a general election.
Tsakalotos spoke after exit polls for Sunday's election showed the governing left-wing Syriza trailing its main rivals by a significant margin.
He told state-run ERT television: "This is a big win for New Democracy. People believed in their program despite it being vague."
Tsakalotos says supporters of Syriza and the government led by Prime Minister Alexis Tsipras "should be proud of our achievements.
He said: "We underestimated the scale of the opposition toward Syriza."
Police say a ballot box was stolen from a polling station in central Athens moments after voting ended in Greece's parliamentary election.
Authorities said a group of young people seized the ballot box and left the polling station inside a school in the capital's central Exarcheia area on Sunday.
Incidents involving anarchist groups are common in that part of Athens.
Exit polls in Greece's general election indicate conservative opposition leader Kyriakos Mitsotakis has won a comfortable victory over left-wing Prime Minister Alexis Tsipras.
The exit polls from Sunday's election predicted Mitsotakis' New Democracy party would win enough seats in Greece's 300-member parliament to form a government without needing to enter a coalition with another party.
The vote was Greece's first parliamentary election since the country emerged from three successive international bailouts and as it continues to struggle from a crippling financial crisis of nearly a decade.
Greeks have begun voting in the first parliamentary election since their country emerged from three successive international bailouts.
The vote is held three months earlier than originally planned after left-wing Prime Minister Alexis Tsipras saw his support erode during European elections.
Opinion polls suggest Greeks are set to defy the recent European trend of increasing support for populist parties, with conservative opposition party leader Kyriakos Mitsotakis a clear favorite to win.
Sunday's vote comes as the country gradually emerges from a brutal nearly decade-long financial crisis that saw unemployment and poverty levels skyrocket, and Greece's economy slashed by a quarter.
Greece was dependent for survival until last summer on international bailouts, and had to impose deep reforms, including massive spending cuts and tax hikes, to qualify for the rescue loans.