A 20-second sample of the song's chorus, which features the lyrics "Even though it kills me that you have to go/ I know I'd be sadder if you didn't hit the road". Melissa Maerz for Entertainment Weekly described Rihanna's execution of the lyrics as "[wailing]."
The song was written by Ester Dean and Alexander Grant, with production helmed by Grant under his production name Alex da Kid. "Farewell" contains lyrics that revolve around saying goodbye to a lover who is not able to be physically present in the relationship for long periods of time.Instrumentation consists of a piano. The song was composed in the key of G major and set in common time signature, and has a moderately slow tempo of 88 beats per minute. Rihanna's vocals span from the low note of G3 to the high note of D5. Jason Lipshutz of Billboard magazine noted that the song's structure was similar to Beyoncé Knowles' song "Halo", while Priya Elan for NME wrote that the song was reminiscent of Rihanna's song "Fire Bomb", from her fourth studio album, Rated R (2009). Lipshutz also noted that Rihanna delivered the bridge with "powerhouse" vocals. A reviewer for Flavour Magazine wrote that Rihanna displayed "great vocals" in the lyric "Somebody's gonna miss you ... Farewell." Melissa Maerz for Entertainment Weekly wrote that Rihanna "wails" the lyrics "'Even though it kills me that you have to go/ I know I'd be sadder if you didn't hit the road."
Music critics were divided on "Farewell"; Rihanna's vocal performance was praised as well as criticized. Kyle Jamon for Parlé Magazine wrote that "Farewell" is a "fitting finish to an album that presents a brand new Rihanna." He praised the song for not incorporating a "morbid" feel or "dark" tones, which were prominent on Rated R. T'Cha Dunlevy for The Montreal Gazette described the song as "epic," and is a "stark contrast" to the songs which appear before it on the album, specifically "Roc Me Out" and "Watch n' Learn". A reviewer for Flavour Magazine described the song as "epic" and "heart-curdling". The reviewer concluded by writing that "Farewell" is a "winning end" to Talk That Talk. Pip Ellwood for Entertainment-Focus wrote that the song "puts paid to any criticism concerning Rihanna's vocal ability." Claire Suddath for Time Entertainment did not praise nor criticize "Farewell," but simply wrote that it is an "obligatory torch ballad that every female pop singer is required to include on an album these days."
Andy Kellman from Allmusic was critical of the ballads "Farewell" and "We All Want Love", labeling the former as "bombastic" and the latter "drippy." Jon Caramanica for The New York Times called "Farewell" the most "bombastic" song on Talk That Talk, and cited his reason as "it's tough to tell if the words have feeling, because Rihanna's voice doesn't." Nathan Slavik for DJ Booth was critical of the song, writing that it lacked any originality. Slavik continued to write that the song is not necessarily bad, but it is "not good in any meaningful way." Simon Price of The Independent slated "Farewell", writing that it is a "shameless rewrite" of Adele's "Someone like You".
Upon the release of Talk That Talk, "Farewell" charted in South Korea and the United Kingdom on the strength of digital download sales. The song debuted on the South Korea Gaon International Chart at number 69 on November 26, 2011, with sales of 6,547 digital downloads. It also debuted on the UK Singles Chart at number 155 in the chart issue December 3, 2011.