Guy Garvey met guitarist Mark Potter at Stand College in 1990 at the age of 16. Potter asked Garvey to sing in a band he was in with drummer Richard Jupp and bassist Pete Turner. Together, the four men formed the band Mr Soft. (The name was later changed to Soft.) Mark Potter's brother Craig Potter joined the band soon after on keyboards. By 1997, they had changed their name a third time to Elbow, signed a deal with Island Records, and recorded their début album with producer Steve Osborne. However, when Island was bought out by major label Universal, the band was dropped in a mass cull and the album never released. They continued to record on the iconic independent label Ugly Man, and released The Newborn EP, and The Any Day Now EP, which were given extensive airplay by BBC Radio 1.

Their debut album, Asleep in the Back, released on V2 in 2001, was hailed as a seminal album of the new millennium, gaining them a Mercury Music Prize nomination and a BRIT Award nomination. Their second album, Cast of Thousands sealed their reputation as innovators in UK music. The title is a reference to their performance at Glastonbury in 2002, when they recorded thousands of people singing, "We still believe in love, so fuck you". That recording was featured on the song Grace Under Pressure.

In 2004, Elbow went on a tour of Cuba, playing songs from Asleep in the Back and 0 at venues in and around Havana. British documentary maker Irshad Ashraf was present on the tour and filmed a large portion of it. The resulting short film was shown at festivals in 2004, but remains commercially unavailable. Their acoustic cover of Destiny's Child's "Independent Women", recorded exclusively for a BBC Radio 1 session, was turned into a popular web animation by Rathergood.com's Joel Veitch. The animation features a band of flat-capped northern kittens "performing" the song. In the same year, their song "Fallen Angel" appeared in the film 9 Songs.

Elbow contributed the song "Snowball" to the 2005 War Child benefit album Help - a Day in the Life. In addition, an unreleased track titled "Beat for Two" was used in the closing titles of the 2004 film Inside I'm Dancing. Garvey also returned to I Am Kloot as co-producer for their single "Maybe I Should". He continues to work closely with Manchester indie label Skinny Dog.

In 2006 the band moved to Fiction Records and completed their fourth studio album, The Seldom Seen Kid in late 2007, which was produced and mixed by keyboard player Craig Potter. The Album released March 2008 has sold over 1 million copies to date. The song "Grounds for Divorce" from this album is featured on the trailer for the Coen Brothers' film Burn After Reading starring Brad Pitt, George Clooney, and John Malkovich.

On 9 September 2008, Elbow won the Mercury Music Prize for The Seldom Seen Kid. The award was presented to them by Jools Holland. The band are currently writing songs and are in the studio recording their fifth album, which is planned for release in early 2011, along with a UK-wide arena tour in March 2011

In 2009, Elbow contributed to War Child's Heroes album, covering U2’s "Running to Stand Still". In May 2009, the band won two prestigious Ivor Novello awards: the song 'One Day Like This' won the main award for Best Song, and 'Grounds for Divorce' was voted Best Contemporary Song

Elbow exclusively performed their album "The Seldom Seen Kid" for BBC Radio 2 and BBC 6 Music with the BBC Concert Orchestra and London-based chamber choir Chantage at the Abbey Road Studios on 17 January 2009 (first broadcast on 31 January 2009).

They opened for Coldplay at several stops on the Viva la Vida Tour's 2009 North American leg. They opened for U2 on 14 August 2009 in Wembley Stadium, London, UK and at the Sheffield Don Valley Stadium, Sheffield, UK.