According to the commision, Mr Kabore, a former Prime Minister, secured 53.5% of the vote on Sunday.
This is the first election since the uprising in 2014 which toppled longstanding President Blaise Compaore.
The Independent National Electoral Commission said that Mr 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.
Mr Diabre has already congratulated Mr Kabore, according to the AFP News Agency.
Roch Marc Christian Kabore, 64, is now living in exile in neighbouring Cote D’ívoire.
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.
Mr Kabore served as Chairman of the ruling Congress for Democracy and Progress Party (CDP) before leaving it in 2014, after opposing plans to extend Mr Compaore’s rule.
