The England captain finished ahead of France international Mbappe, who came second, while Barcelona youngster Yamal claimed third place.
Kane becomes the fifth Englishman to win the Ballon d'Or and the first in 25 years, following Michael Owen's success in 2001. He joins an illustrious list that includes Sir Stanley Matthews, Sir Bobby Charlton and Kevin Keegan.
The 33-year-old's outstanding performances throughout the 2025-26 campaign made him a leading contender for the award.
Kane scored 61 goals and provided seven assists in 51 appearances for Bayern, while adding 11 goals and three assists for England.
He finished as the Bundesliga's leading scorer with 36 goals, scored 14 times in the Champions League and also claimed the European Golden Shoe.
Speaking after receiving the award in London, Kane thanked those who voted for him and recognised the achievements of his fellow nominees.
"Being in London is special, thank you to everyone who voted for me; I'm sure it was tough to pick," he said.
"Congratulations to all the winners and nominees; it's a real showing of what hard work and determination can do."
Kane also paid tribute to his Bayern team-mates, stressing that their contribution had been crucial to his individual success.
"Without you guys and the rest of the team, it wouldn't be possible; the way you guys push me, the way we compete. So thank you very much," he said.
England manager Thomas Tuchel, who previously coached Kane at Bayern, described the award as deserved recognition of the striker's remarkable consistency.
"Congratulations Harry on a deserved Ballon d'Or! I ran out of superlatives to describe your performances a long time ago, but I'm delighted to see that you have now been formally recognised by the football world," Tuchel said.
Tuchel also highlighted the significance of Kane becoming the first English winner since Owen.
"To become the first Englishman to win this huge honour in 25 years makes it extra special and we are lucky to have you as our leader," he added.
The England manager believes Kane will enjoy the achievement with his family before returning his attention to the task of delivering more goals and victories.