Announced in December 2018, the song was released for digital download and streaming on 24 January 2019 through Warner Bros. Records as the soundtrack's lead single.

In the song, Lipa references 1980s AIDS activist group ACT UP and sings about new beginnings and society using their voices to fight for what they believe in.

At the end of 2018, Dua Lipa was contacted about an opportunity to create a song for the new film Alita: Battle Angel, which James Cameron and Robert Rodriguez had been working on.

[4] The film team thought that Lipa would be a perfect fit for Alita: Battle Angel after seeing her music video for "New Rules".

[6] Lipa wrote "Swan Song" alongside Justin Tranter, Kennedi Lykken, Mattias Larsson, Robin Fredriksson and Tom Holkenborg.

[31][32] While promoting the song, Lipa wanted viewers to find a piece of themselves in Alita and inspire one to do good in everyday life.

[4] "Swan Song" was included as the closing track on physical releases of the Milan Records-released Alita: Battle Angel soundtrack.

[34] An extended play featuring remixes by DJ Shadow and NastyNasty, Maya Jane Coles, aboutagirl and Calibre was released on 12 April 2019.

[35] In Time, Raisa Bruner viewed "Swan Song" as a "clear battle anthem" where Lipa's "mellifluous" voice adds "weight and smoothness, and a welcome human element".

[15] Writing for The New York Times, Jon Pareles compared the backup chants to "remnants of past civilizations" and thought the song "puts human aspiration in electronic armor".

Additionally, he said the song "feels properly high stakes, but also kind of weird and murky until its head-rattling chorus kicks in".

[19] Chris DeVille of Stereogum complimented how Lipa experimented with the track and compared it to Lorde's "Yellow Flicker Beat" (2014).

[38] In Popjustice, Peter Robinson praised the "creative and luxurious production" that is "sparse where it needs to be and full of dramatic and unpredictable little flourishes" while also complimenting how the song fades out at the end.

[22] Writing for Audacy, Michael Cerio viewed the song as a "sweeping epic, building like a battle hymn into a post-apocolyptic banger".

[41] The British Phonographic Industry (BPI) awarded the song a silver certification in November 2021 for selling 200,000 track-equivalent units in the UK.

[48] In 2020, the song was awarded a gold certification from the Polish Society of the Phonographic Industry (ZPAV) for track-equivalent sales of 10,000 units in Poland.

[50][51] In the United States, the song spent five weeks on the Billboard Bubbling Under Hot 100 Singles chart, peaking at number four.

The only time Lipa had to rehearse for the videos shoot was while she was in Toronto writing for her album so she would spend the entire day in the studio and then go and practice the moves every night for two to three hours.

[58] Robinson thought it marked "the best rubbish dump-based pop video" since "Keep Your Head Up" (2009) by Girls Can't Catch.