The synth line was written around 1981 by Eddie Van Halen but it was refused by the other members of the band. In 1983, producer Ted Templeman asked Roth to take a listen to the unused song idea. Riding around in the back of his 1951 Mercury, with band roadie Larry Hostler driving, Roth listened repeatedly to the song. To come up with a lyric for it, he remembered seeing a television news report the night before about a man who was threatening to commit suicide by jumping off a high building. Roth thought that one of the onlookers of such a scene would probably shout "go ahead and jump". Roth bounced this suggestion off Hostler who agreed it was good. Instead of being about a threatened suicide, the words were written as an invitation to love. Roth later told Musician magazine that Hostler was "probably the most responsible for how it came out."
Ted Templeman recalls that "'Jump' was recorded at Ed's studio. Donn and Ed put the track down alone in the middle of the night. We recut it once in one take for sonic reasons. Dave wrote the lyrics that afternoon in the backseat of his Mercury convertible. We finished all vocals that afternoon and mixed it that evening".
The song was listed by The Rock and Roll Hall of Fame and Museum as one of the "500 Songs that Shaped Rock and Roll."
Live performances of "Jump" are preceded by Eddie's synthesizer solo "1984". During the reunion tour with Roth, the two songs were used for the band's encore. Roth often waved a large red flag during the synth section while the stage was still coated in dark cover lights.