Craig and Bellucci are seen making out as Smith croons in front of Union Jack-draped coffins interspersed with scenes from the film.
The 23-year old singer told Entertainment Tonight that he was nervous about the song and thought his fans would dislike the new single.
"I keep looking at that Wikipedia page and just seeing my name on it -- and it's unreal," Craig told ET.
"Writing's on the Wall" became the first ever James Bond theme to reach the No.1 slot on the U.K. Billboard charts following its release.
Smith announced in September that he'd been tapped to write and sing the theme calling the opportunity "one of the highlights" of his career.
He also became the second male in the history of the franchise to sing its theme, following Tom Jones' "Thunderball" in 1965. Smith's song was originally released online on Sept. 25.
Craig, 47, has played the iconic British spy four times in multiple James Bond movies, beginning with 2006's Casino Royale. The current film, Spectre, hits theaters Nov. 6.
Italian actress and fashion model Bellucci plays the oldest Bond girl in the franchise at age 51. In February, she told ET Online that she was shocked when director Sam Mendes told her she had landed the role, initially thinking she was going to replace Judi Dench, who played Bond's commander, M, in several films. Prior to Bellucci, the oldest Bond girl was Honor Blackman, who played Pussy Galore in the 1964 film Goldfinger at the age of 39. Runner-ups include Halle Berry at 36 and Ursula Andress at 26 and 31.