It says Kabore, a former prime minister, secured 53.5% of the vote on Sunday.
It was the first election since last year's popular uprising which toppled longstanding President Blaise Compaore.
The vote was due to have been held last month but was delayed by a failed coup in September led by members of the elite presidential guard.
Compaore, 64, is now living in exile in neighbouring Ivory Coast.
The Independent National Electoral Commission says Kabore, 58, won the elections outright, and there is no need to hold a second round.
It says his main rival, former Economy and Finance Minister Zephirin Diabre, gained 21.6% of the vote.
Diabre has already congratulated Kabore, according to the AFP news agency.
Kabore served as chairman of the Congress for Democracy and Progress party (CDP) before leaving it in 2014, after opposing plans to extend Compaore's rule.
On Sunday, long queues were reported outside many polling stations.
Security was also raised, with up to 25,000 troops and police deployed across the country and foreign observers oversaw the poll.
The election was meant to mark the end of the transitional period following Compaore's removal.
Compaore was forced from office by street protests in October 2014 over his plans to serve another five-year term. He had been in power for 27 years.
A transitional government was installed but the country was thrown into turmoil again in September when members of the elite presidential guard led a short-lived coup. The attempt failed and the guard was disbanded.
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