The album was compiled after McCartney's decision to leave EMI's American label, Capitol, for a six-year stay with Columbia (United States and Canada only), though he remained with EMI worldwide during his US sabbatical from Capitol. Wings Greatest is notable for including many of McCartney's post-1970 single-only releases, including "Another Day" (actually a "Paul McCartney" song, not a "Wings" recording), "Live and Let Die", "Junior's Farm", "Hi, Hi, Hi" and "Mull of Kintyre". In addition to "Another Day", "Uncle Albert/Admiral Halsey" was originally credited to "Paul & Linda McCartney" and from their 1971 album Ram.
Despite the fact that McCartney had amassed enough hits by late 1978 to fill a double album of hits, he kept it down to a single disc for commercial reasons. Thus, several songs would be overlooked for Wings Greatest. Indeed, not one song was excerpted from 1975's Venus and Mars, despite "Listen to What the Man Said" being a number 1 US hit. The album was promoted by a TV commercial in the UK, which featured several members of the public (played by actors) singing Wings tunes in public places. At the end a dustman, waiting in his lorry at a set of traffic lights (in Abbey Road), sings to himself an out of tune rendition of "Band on the Run", at which point Paul, Linda and Denny pull up alongside and Paul shouts out "You're a bit flat mate!". The driver leans out his window and says "Funny, I only checked them this morning!"
The Bulgarian pressings of the album did not include the song "Live and Let Die". In 1993, Wings Greatest was remastered and reissued as part of "The Paul McCartney Collection".
The front of the album cover depicts a chryselephantine (gold and ivory) statuette in the snow. The statuette of Semiramis was created by famed Art Deco sculptor Demetre Chiparus. Having bought it, Linda wanted the flying lady photographed in the snow, so on 14 October 1978 she flew the statuette and photographer Angus Forbes to the Alps, where a snowdrift was created and the photograph was taken from a helicopter.
The rear cover depicts the record covers of the twelve releases, mostly singles, from which each of the Greatest's songs were taken, in columns on either side of the album. In the middle is a photograph of Paul, Linda, and Denny Laine. The background is another scene of the Alps.
The statuette also appears on the inner sleeves of the original vinyl, as well as on the record's labels. It can also be seen on the album cover of Back to the Egg in the background, on the mantelpiece.