The Central Election Commission said Jeenbekov had won around 55 per cent of the vote, with oligarch opponent Omurbek Babanov taking more than a third of the ballot.
"Jeenbekov is leading," CEC head Nurzhan Shayldabekova told reporters in the capital Bishkek, saying 95 per cent of the ballots had been counted.
Preliminary figures showed turnout at just over 50 per cent.
"Our campaign took great pleasure in the favorable results announced by the CEC," said Konduz Joldubayev, a spokesman for Jeenbekov.
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Pre-election campaigning was overshadowed by an apparent smear campaign against Babanov, who leads the parliament's second largest party, and suspicions that Jeenbekov could benefit from government patronage.
Jeenbekov is a close ally of incumbent president Atambayev, 61, who chose to respect a single, six-year presidential term and step down.
Resource-poor Kyrgyzstan is seen as the most democratic state in Central Asia, a predominantly authoritarian region, but it has also been the most politically volatile in recent times.
The Muslim-majority country experienced two revolutions that unseated presidents in 2005 and 2010 followed by ethnic violence that left over 400 people dead.