Jeenbekov, 59, a close ally of outgoing Almazbek Atambayev, swore to protect the "unity of the country" as he accepted the national flag and donned a breastplate signifying the presidency.
The boom of artillery fire marking the power transfer was audible across Bishkek, the capital of the majority-Muslim country of six million.
The former Soviet republic saw its first two presidents overthrown in revolts in 2005 and 2010, with ethnic violence leaving hundreds dead after the second revolt.
Speaking in both Kyrgyz and Russian, a notably nervous Jeenbekov cited inspiration from the country's mythical hero Manas, the main character of an oral epic, and pledged to battle systemic corruption.
"A ruthless fight against corruption has begun. Conditions have been created to purify society," said Jeenbekov, who began working life as school teacher.
Under Atambayev, who was constitutionally restricted to a single six-year-term in office, the country enjoyed a period of relative stability, albeit without real reforms.
After embracing his political ally, the controversial outgoing leader sounded a triumphant note, describing his time in office as one that spared the country from collapse.
"Foreign political scientists said we would fall apart, but it didn't happen. Now we are an independent country. I thank my people," Atambayev said.
Jeenbekov scored 54 percent of the October 15 ballot viewed as Kyrgyzstan's most competitive election since independence, with oligarch opponent Omurbek Babanov taking more than a third of votes cast.
But monitors said the vote was marred by evidence of voter intimidation and other forms of administrative leverage that appeared to benefit Jeenbekov's campaign.
Kyrgyz authorities earlier this month pressed ahead with a criminal case against Babanov over remarks he made in a neighbourhood inhabited by an ethnic minority during a bitter electoral campaign.
The 47-year-old former oil trader, who, like Jeenbekov, served as a prime minister during Atambayev's tenure, resigned his position as head of the parliament's second largest party earlier this month.
Atambayev steered a strongly pro-Russian foreign policy course, and while those relations are likely to remain unchanged, successor Jeenbekov faces an uphill struggle to repair ties with oil-rich neighbour Kazakhstan.
The two countries have been locked in dispute ever since a spat that began with Kazakh president Nursultan Nazarbyev appearing to endorse Jeenbekov's main electoral rival escalated into a full-blown trade war.
Kyrgyzstan hosts a Russian military base and is a member of a Moscow-led trade bloc, but leans heavily on next-door China for loans and investments.
Kyrgyzstan is alone in hosting competitive votes in Central Asia, a region defined by corruption and an authoritarian political culture.
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