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. BBC repots.
Mr Compaore, 64, is now living in exile in neighboring Ivory Coast.
The Independent National Electoral Commission says 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.