Nils Petter Molvær was born September 18, 1960, in Langevåg, the main village on the island of Sula off Norway's western coast, and grew up there before leaving at nineteen to study jazz at the Trondheim Musikkonservatorium from 1980 to 1982. The trumpet came first, but the thing that shaped his eventual sound was hearing Jon Hassell and Brian Eno's Fourth World, Vol. 1: Possible Musics, which he later said showed him "it's possible to do something unique with the trumpet without fighting with it." He built his early tone by listening past jazz trumpet altogether, to South Indian bansuri players such as Hariprasad Chaurasia and to shakuhachi and ney flute recordings.

Through the 1980s Molvær worked as one of Oslo's busiest session players, turning up on Norwegian pop, folk and singer-songwriter records by Anne Grete Preus, Jan Eggum, Bjørn Eidsvåg and Sissel Kyrkjebø alongside his jazz work with Jon Eberson's groups and Jon Balke's big band Oslo 13. His defining band of the decade was Masqualero, formed in 1983 as the Arild Andersen Quintet and renamed after the Wayne Shorter tune that gave its debut album its title. The group paired Molvær with bassist Arild Andersen, drummer Jon Christensen, saxophonist Tore Brunborg and keyboardist Jon Balke, and Andersen insisted it operated without a designated soloist or leader. After the self-released debut on Odin in 1983 the band moved to ECM for Bande À Part (1986), Aero (1988, with guitarist Frode Alnæs replacing Balke) and the quartet date Re-Enter (1991), three of the four winning Spellemannsprisen awards. Molvær's other ECM appearances in this stretch were with singer Sidsel Endresen on So I Write (1990) and Exile (1994), and as co-leader of the trumpet-and-percussion duo record Hastening Westward (1995) with the American percussionist Robyn Schulkowsky.

Khmer, recorded at Lydlab in Oslo across 1996 and 1997 and issued by ECM in October 1997 (ECM 1560; the US release followed in 1998), changed the shape of his career and of the label's reputation at the same time. Molvær played trumpet, guitar, bass and samples himself, built the tracks around Rune Arnesen's drumming and Eivind Aarset's treated guitars, and brought in Ulf W. Ø. Holand as co-producer with Manfred Eicher. The result folded drum and bass, dub, ambient and hip-hop production into ECM's austere recorded aesthetic, on a label whose catalogue was then defined by Keith Jarrett and Pat Metheny. AllMusic's Christian Genzel, awarding four and a half stars, called it the most unusual album ECM had ever released. It sold roughly 250,000 copies worldwide, an extraordinary figure for a jazz debut, and became the standard reference point for the "future jazz" and nu-jazz tags that European critics applied to the scene that followed.

He stayed with ECM for the remix set Khmer (The Remixes) and the Ligotage maxi-single, then for Solid Ether (May 5, 2000, ECM 1722), recorded in Oslo in 1999 with Aarset, bassist Audun Erlien, drummers Arnesen and Per Lindvall, DJ Strangefruit and Endresen. Robert Christgau graded it an A, writing that Molvær "immerses in chaos and comes out beautiful," and All About Jazz's Chris Slawecki described it as a meltdown of classic jazz trumpet into techno and drum and bass. Molvær then left the label, later telling Innerviews he had found it arrogant that ECM never asked him where his music should be placed, having blocked compilation appearances beside Björk and Massive Attack, two direct inspirations for Khmer. He set up his own imprint, Sula Records, distributed through Universal and EmArcy, and made NP3 (September 9, 2002), the live Streamer (2004), Er (2005), the remix album Remakes (2005), Re-Vision (2008) and Hamada (2009). Thirsty Ear handled the American side of the catalogue, releasing An American Compilation in June 2006, a set Molvær selected himself to introduce the previous decade of work to US listeners. He also wrote his first feature score in this period, for Stéphan Guérin-Tillié's Edy (2005).

From 2011 the records got harder and more physical. Baboon Moon (September 16, 2011, Columbia/Sony) was cut as a trio with guitarist Stian Westerhus and drummer Erland Dahlen at Ocean Sound Recordings on Giske, near Molvær's home island. He then signed to Sony's revived Okeh imprint for Switch (April 7, 2014), built with Dahlen, pedal-steel player Geir Sundstøl and pianist Morten Qvenild, and Buoyancy (September 2, 2016), a quartet date with Dahlen, Sundstøl and bassist Jo Berger Myhre that took Spellemannsprisen's jazz award. The collaborations ran in parallel: 1/1 (2013) with Berlin dub-techno producer Moritz von Oswald, Nordub (2018) with Sly Dunbar and Robbie Shakespeare plus Aarset and Vladislav Delay, and SulaMadiana (2020) with percussionist Mino Cinelu, named for Molvær's island and Manu Dibango's Cameroonian home. In 2021 he and the German free-jazz saxophonist Peter Brötzmann shared the European Film Award for Best Composer for Sebastian Meise's Great Freedom.

His recent work has moved between the ensemble records Stitches (August 27, 2021, with Johan Lindström, Berger Myhre and Dahlen) and the orchestral Certainty of Tides (October 6, 2023) with the Norwegian Radio Orchestra under Ingar Bergby. In 2025 he signed to the British label Edition Records, which released Khmer Live in Bergen on September 12 of that year, a concert reading of the 1997 album with Aarset, Erlien, Arnesen, Lindvall, DJ Pål "Strangefruit" Nyhus and Jan Bang. A new studio album, Be Quiet, is scheduled for Edition in July 2026. His awards include the first Kongsberg Jazz Award in 1996, Spellemannsprisen in the open class in 1997, 2000 and 2005, Gammleng-prisen in 1998, Buddyprisen in 2003 and Edvardprisen in 2010.

Molvær plays a small, dark, breathy trumpet sound, usually processed through delay, distortion and looping pedals, and treats the horn less as a bebop instrument than as a single sustained voice floating over programmed rhythm. The lineage runs from Miles Davis's electric period through Jon Hassell's "Fourth World" trumpet to the dub production of Bill Laswell, whose Material and Golden Palominos records Molvær has named as early reference points and with whom he has since recorded repeatedly. He composes in layers rather than in heads and choruses, building tracks in the studio from samples, loops and treated guitar and only then finding a trumpet line for them, which is why his catalogue sits as comfortably in electronic listings as in jazz ones. Khmer gave European critics the category they had been reaching for, and Molvær became the fixed point for a Norwegian generation, Bugge Wesseltoft, Eivind Aarset, Jan Bang and the Punkt festival circle among them, that worked the same seam between improvisation and club production. His own site describes him as a quiet but foundational figure in contemporary European jazz, and the description holds up: the sound he arrived at on one 1997 record is now the house style of a whole regional scene.