He set upon writing music full-time and eventually caught the attention of former BMI executive Christian Ulf-Hansen, who became his manager. Universal released his first album, Poetry & Aeroplanes, in 2003, while Teitur found himself opening for Suzanne Vega, Glen Phillips, Aimee Mann, and John Mayer as well as playing over 300 shows through the following year.

In April 2006, Teitur parted ways with Universal due to months of legal problems and creative differences. His second album, Stay Under the Stars, was released in May 2006 in Scandinavia on Playground Music and produced by Martin Terefe (a-ha, Ron Sexsmith). A record in the Faroese language titled Káta Hornid followed a year later. In 2008, The Singer arrived via Playground, German label Edel Records, and California label SideCho Records, growing his audience, and in 2009, All My Mistakes was issued internationally by A&G. He followed it with the live album Night at the Opera (for Ear Music) and the studio LP Let the Dog Drive Home, both in 2010. The latter was originally released by Playground, then reissued a few months later by Arlo & Betty Recordings, which also released his 2013 album Story Music.

In 2016, the singer/songwriter partnered with classical composer and frequent indie-music collaborator Nico Muhly (Björk, the National) for Confessions, a collection of songs recorded with the ensemble Holland Baroque Society, and his debut on Nonesuch. ~ Kenyon Hopkin & Marcy Donelson