The conservative New Democracy party seeks to recover from its heavy election defeat in September, when Greeks re-elected Tsipras' Syriza party amid capital controls on bank deposits and a harsh third bailout with the country's foreign lenders.
Mitsotakis, a 47-year reformist lawmaker and scion of one of Greece's most influential political families, is expected to pile pressure on 41-year-old Tsipras ahead of a crucial parliamentary vote on pension reform, as part of the first review of Greece's bailout programme.
Mitsotakis ran second to Vangelis Meimarakis in the first round of the party leadership election on Dec. 20, contested by four candidates, and was ahead in Sunday's runoff with 51 percent of the vote with most of the vote counted.
"United, we move ahead to the creative rejuvenation and expansion (of the party), so that New Democracy becomes the big centre-right party ... that will provide a reliable alternative for the country's governance," he said when victory was clear.
The final result will be announced today.
New Democracy ruled Greece alone from 2004 to 2009 but has seen its popularity wane during the debt crisis. The party lost an election in January that first brought Tsipras to power and a second one in September.
An ex-banker who has been a critic of trade union practices and state waste, Mitsotakis has called Tsipras "a liar" but also hinted that he could cooperate with him on national issues on specific terms.
His father Constantinos served as prime minister from 1990 to 1993 and his older sister, Dora Bakoyianni, was foreign minister from 2006 to 2009.
Meimarakis, a political veteran, took over as interim party leader in July from former prime minister Antonis Samaras, who quit in response to a strong 'No' vote in a referendum on the terms of Greece's third international bailout.
But he stepped down in November, taking responsibility for a botched ballot to choose a new party chief.
New Democracy initially opposed the country's international bailouts. But after winning a parliamentary election in 2012 and forming a coalition with the Socialist PASOK party, it brought in austerity and unpopular reforms demanded by the country's international lenders.
On Sunday's, anti-establishment protesters stormed into a poll station and threw paint in an attack against the conservative party, which they accused of links with "corrupt capitalists".