Jakob Bro was born on April 11, 1978, in Copenhagen. His father led a big band and taught music, so instruments were always around the house, and Bro has said he played tambourine with the band before he could walk. He took up trumpet next, playing in a youth orchestra, in the big band and in church. In sixth grade he started listening to Jimi Hendrix and moved to guitar, for a while playing both instruments before guitar won out, and in high school he was absorbed by fusion records his father brought home by John Scofield and Pat Martino. He left school early to concentrate on music, studied at a jazz school in Aarhus and, at 17, at the Royal Academy of Music there, where he met the drummer Rune Kielsgaard and the bassist Eske Nørrelykke. The three then went to the Berklee College of Music in Boston.

Even before leaving Denmark Bro had been noticed by players he admired, among them Michael Brecker and the pianist Carsten Dahl, and he had played with the saxophonist Jakob Dinesen. At a Copenhagen gig with Dinesen the American guitarist Kurt Rosenwinkel, whom Dinesen knew from Berklee, sat in and afterwards told Bro to come to New York. First, though, Bro returned to Copenhagen from Boston and formed the quartet Beautiful Day with Dinesen; its album Beautiful Day! (2002) brought him the New Danish Jazz Artist of the Year prize at the Danish Music Awards, which his own biography dates to 2003. He then moved to New York, where he continued his studies and took lessons from the guitarist Steve Cardenas and the bassist Ben Street, living for a time in Street's apartment. Street introduced him to the saxophonists Mark Turner and Chris Cheek and to the bassist Larry Grenadier.

The decisive connection was with the drummer Paul Motian. Bro has said he spent six months learning Motian's repertoire so thoroughly that he could play the tunes from memory when he started with the band. He can be heard with Motian's three-guitar band on Garden of Eden, recorded in November 2004 at Avatar Studios in New York and released by ECM in February 2006, alongside Ben Monder, Steve Cardenas, Cheek, Tony Malaby and the bassist Jerome Harris. He was also the guitarist in the trumpeter Tomasz Stańko's quintet on Dark Eyes (ECM, recorded April 2009 at Studios La Buissonne in France), where, as he later recalled, there was at first no obvious room for a guitar and he had to make one. The Motian connection also introduced him to the alto saxophonist Lee Konitz, according to The Guardian, and the guitarist Bill Frisell became a regular partner on his own records.

His own records began on Loveland, the Copenhagen label he runs: Daydreamer (2003), Sidetracked (2005), Pearl River (2007, with Motian, Street, Cheek and Turner), The Stars Are All New Songs Vol. 1 (2008, with Frisell, Rosenwinkel, Motian and others), then Balladeering (2009, with Konitz, Frisell, Street and Motian), Time (2011, with Konitz, Frisell and the bassist Thomas Morgan) and December Song (2013, adding the pianist Craig Taborn). Those last three were nominated together for the Nordic Council Music Prize in 2014. Balladeering also had a companion documentary DVD, Weightless, about the recording session. In 2012 he released Bro/Knak, a double album made with the Danish electronic producer Thomas Knak whose cast, according to German Wikipedia, also included the pianist Paul Bley, the trumpeter Kenny Wheeler and Frisell.

His first record as a leader for ECM was Gefion (recorded November 2013 at Rainbow Studio in Oslo, released February 6, 2015), a trio with Morgan and the Norwegian drummer Jon Christensen. It was followed by Streams (2016, recorded in November 2015 in Pernes-les-Fontaines, France, with Morgan and the drummer Joey Baron and dedicated to Motian), Returnings (2018, recorded in Oslo with Morgan, Christensen and the Danish trumpeter Palle Mikkelborg), the live Bay of Rainbows (2018, from two nights at the Jazz Standard in New York in July 2017, with Morgan and Baron), and Uma Elmo (2021, with the Norwegian trumpeter Arve Henriksen and the drummer Jorge Rossy). In November 2021 he recorded Once Around the Room: A Tribute to Paul Motian in Copenhagen with the tenor saxophonist Joe Lovano, a septet with two bassists (Morgan and Grenadier) and two drummers (Baron and Rossy), released by ECM in November 2022. Strands (2023), a live trio set with Mikkelborg and the percussionist Marilyn Mazur, was recorded at the Danish Radio Concert Hall in February 2023. In 2024 ECM issued Taking Turns, a session cut in March 2014 at Avatar Studios in New York with Konitz, Frisell, the pianist Jason Moran, Morgan and the drummer Andrew Cyrille, and held back for a decade before its release on November 29, 2024. He has led annual engagements at the Village Vanguard in New York since 2020.

Recent releases have come mainly from Loveland. The film Music for Black Pigeons, directed by Jørgen Leth and Andreas Koefoed, follows him and his ensembles and was shown out of competition at the Venice Biennale in 2022; its soundtrack came out in 2024. Loveland has also issued Live at the Village Vanguard with Lovano (recorded May 26 to 28, 2023); Murasaki (2025, with the trumpeter Wadada Leo Smith and the drummer Marcus Gilmore, recorded January 11, 2025 in New York); The Montclair Session (2025, recorded in 2022 with Smith, the pianist Marilyn Crispell and Cyrille); two duo records with the Japanese percussionist Midori Takada, Until I Met You (2025) and From Such a Blue Sky (2026), both recorded in Tokyo; and 8 (August 2026), an eight-piece ensemble date with Taborn, Gilmore, Cheek, Grenadier and the drummer Brian Blade, playing mostly music by Motian and Bro. A record with the saxophonist Charles Lloyd, Bjerge, Strand, with Grenadier and Rossy, is listed for release on November 13, 2026. ECM lists a European tour by the trio with Baron and Morgan from November 26 to December 3, 2026.

Bro has won six Danish Music Awards between 2003 and 2016, the Carl Prize for Jazz Composer of the Year in 2013 and 2016, and the Jazznyt Prize in 2013 for December Song, and he was named Rising Star guitarist in the 2018 DownBeat International Critics Poll. Music for Black Pigeons earned a 2024 nomination for Danish Music Award Jazz Composer of the Year, and the Danish Artist Association gave him an honorary award in 2023.

Bro writes short, song-shaped pieces in which a single melody carries the mood and the band is left room to decide what happens around it. He has said he would rather play a few choruses that tell a story than extend a solo, and he often drops solos altogether when a tune does not need one. His tone is clear and sustained, often a shimmer of overlapping guitars, and in a trio he tends to keep the volume low. A critic for Der Standard described his compositions as minimalist yet highly melodic. Early listening to Hendrix, Scofield and Martino gave way to a taste for classical pianists such as Glenn Gould and Sviatoslav Richter and for Bach and Chopin on guitar, and he has described Konitz as someone who seems to sing from the inside, so that a slip hardly matters. He credits time with Paul Motian and Tomasz Stańko with teaching him how to find a place for the guitar in other people's bands. Several of his best-known records, including Time and December Song, are drummerless, and the music sits closer to the chamber side of the ECM aesthetic than to bop. The Guardian chose Taking Turns as its jazz album of the month for January 2025 and credited Konitz for showing Bro how to lead an improvisers' band that plays composed music loosely.