The video shows snippets of the film featuring Bond actor Daniel Craig, Italian actress Monica Bellucci and French actress Lea Seydoux.
Smith, 23, is the first British male solo artist to record a Bond song since Tom Jones’ Thunderball track in 1965.
He co-wrote the single with fellow Grammy Award winner Jimmy Napes, with whom he worked on his best-selling 2014 debut album In the Lonely Hour.