The Bayern Munich striker became the first Englishman in 25 years to lift the award, following Michael Owen in 2001.
Kane scored 73 goals for club and country over the year, helping Bayern to win a league and cup double and taking England to the World Cup semi-finals.
"Wow! I am almost speechless," said the former Tottenham forward. "Being here in London has made it extra special (...) a good omen for me tonight. Thank you to everyone who voted for me.
"Some world-class players in the room tonight. Congratulations to all the winners and nominees tonight."
Earlier, Spain's Alexia Putellas won the women's Ballon d'Or and Yamal was named men's young talent of the year.
Mbappe's wait to win the Ballon d'Or goes on despite his prolific year for France and Real Madrid.
Luis de la Fuente beat Paris Saint-Germain's Luis Enrique and Arsenal's Mikel Arteta to be named men's coach of the year after leading Spain to World Cup glory.
Barcelona's Pere Romeu won the women's coach of the year award, while Arsenal winger Bukayo Saka was handed the Socrates award for his humanitarian work.
PSG missed out on the main individual awards despite winning a second consecutive Champions League title, but were named men's club of the year.
Spain's Unai Simon and Cata Coll were named best men's and women's goalkeepers, respectively.