Terence Oliver Blanchard was born on March 13, 1962, in New Orleans, the only child of Wilhelmina and Joseph Oliver Blanchard; his father was a manager at an insurance company and an amateur opera singer. He began on piano at five and switched to trumpet at eight after hearing Alvin Alcorn play at his school. At summer music camps he played alongside two childhood friends, trumpeter Wynton Marsalis and saxophonist Branford Marsalis. He attended the New Orleans Center for Creative Arts, where his teachers included Roger Dickerson and Ellis Marsalis, and from 1980 to 1982 studied at Rutgers University with saxophonist Paul Jeffrey and trumpeter Bill Fielder, touring with the Lionel Hampton Orchestra while still a student.

In 1982, just before he turned 20, he left Rutgers to join Art Blakey's Jazz Messengers. Wynton Marsalis recommended him as his replacement, and Blakey named him the band's musical director. With fellow New Orleanian Donald Harrison in the front line, he toured widely with the Messengers and appears on Oh-By the Way (1982), New York Scene (1984) and Blue Night (1985). The two also ran a quintet of their own, which recorded New York Second Line for Concord in 1983. After they left the Messengers in 1986, when Wallace Roney took over the trumpet chair that September, the Harrison/Blanchard quintet continued for Columbia, with Mulgrew Miller on piano and Ralph Peterson on drums for Nascence (1986) and pianist Cyrus Chestnut and drummer Carl Allen for Crystal Stair (1987) and Black Pearl (1988).

In 1989 Blanchard stepped away from performing for a time to correct his embouchure, and in 1991 Columbia released his self-titled debut as a leader, which reached number 3 on Billboard's jazz chart. He had by then played on the soundtracks of Spike Lee's Do the Right Thing (1989) and Mo' Better Blues (1990), and Lee hired him to compose the score for Jungle Fever (1991). He went on to score most of Lee's films, among them Malcolm X (1992), Clockers (1995), Summer of Sam (1999), 25th Hour (2002), Inside Man (2006), BlacKkKlansman (2018) and Da 5 Bloods (2020), and has written more than 80 film and television scores in all, including work for directors Kasi Lemmons, Gina Prince-Bythewood and Regina King. BlacKkKlansman and Da 5 Bloods each earned him an Academy Award nomination for Best Original Score. His Columbia albums ran alongside the film work: Simply Stated (1992), The Malcolm X Jazz Suite (1993), In My Solitude: The Billie Holiday Songbook (1994), made with vocalist Jeanie Bryson, Romantic Defiance (1995) and The Heart Speaks (1996), a Latin jazz date with Ivan Lins and percussionist Paulinho da Costa that drew a Grammy nomination. At Sony Classical he made Jazz in Film (1999), which featured Joe Henderson and the pianist Kenny Kirkland; Wandering Moon (2000), which brought a Grammy nomination and DownBeat's Artist of the Year honor; and Let's Get Lost (2001), a set of Jimmy McHugh songs with guest vocalists Diana Krall, Jane Monheit, Dianne Reeves and Cassandra Wilson.

He signed with Blue Note in 2003 and released Bounce, co-produced by Michael Cuscuna, with Aaron Parks on piano, Lionel Loueke on guitar, Robert Glasper on electric piano and Eric Harland on drums, followed by Flow (2005), produced by Herbie Hancock. Between the two he played on McCoy Tyner's Illuminations (Telarc, recorded November 2003) with Gary Bartz, Christian McBride and Lewis Nash, which won the Grammy for Best Jazz Instrumental Album. After Hurricane Katrina he scored Lee's HBO documentary When the Levees Broke: A Requiem in Four Acts (2006), appearing on screen with his mother as they searched for her destroyed home. His next album, A Tale of God's Will (A Requiem for Katrina) (Blue Note, August 14, 2007), reworked that score with new pieces and won the Grammy for Best Large Jazz Ensemble Album. Choices (Concord, 2009), Chano y Dizzy! (Concord, 2011), a duet album with conga player Poncho Sanchez on the music of Dizzy Gillespie and Chano Pozo, and Magnetic (Blue Note, 2013) followed. For Disney's The Princess and the Frog (2009) he played all the trumpet parts for the alligator character Louis and voiced the bandleader Earl.

In 2015 he introduced a new electric group, the E-Collective, on Breathless (Blue Note, May 26, 2015). Its core was Fabian Almazan on keyboards, Charles Altura on guitar, Donald Ramsey on bass and Oscar Seaton on drums, and the songs responded to the death of Eric Garner and the "I Can't Breathe" protests. Live (April 20, 2018) used the same band with David Ginyard replacing Ramsey on bass, and Absence (August 27, 2021), recorded with the Turtle Island Quartet, was a tribute to his mentor Wayne Shorter. Breathless and Absence were both nominated for the Grammy for Best Jazz Instrumental Album, and "Blut und Boden (Blood and Soil)", from his BlacKkKlansman score, won the Grammy for Best Instrumental Composition at the 2019 ceremony.

Blanchard has also become an opera composer. Champion, with a libretto by Michael Cristofer about the boxer Emile Griffith, premiered at the Opera Theatre of Saint Louis on June 15, 2013. Fire Shut Up in My Bones, with a libretto by Kasi Lemmons based on Charles M. Blow's memoir, premiered there on June 15, 2019, and opened the Metropolitan Opera's 2021-22 season on September 27, 2021, the first opera by a Black composer in the company's history. Champion reached the Met in April 2023, and the Met's recordings of both operas won the Grammy for Best Opera Recording, at the 2023 and 2024 ceremonies. The Recording Academy lists seven Grammy wins for him in total.

He has held a series of educational and programming posts. He became artistic director of the Thelonious Monk Institute of Jazz (later renamed for Herbie Hancock) in 2000 and pressed for the program's move to New Orleans after Katrina. He was named artistic director of the Henry Mancini Institute at the University of Miami in 2011 and a visiting scholar in jazz composition at the Berklee College of Music in 2015, and he held an endowed chair in jazz studies at UCLA from 2019 to 2023. In 2023 SFJAZZ named him its Executive Artistic Director, a post that its staff page still listed him in as of November 2026. He was named a 2024 National Endowment for the Arts Jazz Master.

Blanchard's trumpet playing comes out of the hard bop and post-bop tradition, and his composing carries that harmonic language into larger forms: The Malcolm X Jazz Suite, a Katrina requiem for jazz ensemble and strings, and two operas. Entertainment Weekly called him central to a resurgence of jazz composition for film. His albums range from the quintet jazz of the Harrison/Blanchard years through the standards and ballads of In My Solitude and Let's Get Lost to The Heart Speaks, a Latin jazz collaboration with Ivan Lins, and, with the E-Collective, an electric band that adds synthesizers, effects and spoken word and takes up contemporary politics. His teachers and elders recur in his story: Ellis Marsalis in New Orleans, Art Blakey in the Messengers, and Wayne Shorter, whom Absence honors as a mentor. The Harrison/Blanchard quintet was credited with influencing a younger generation of musicians that included Christian McBride, Nicholas Payton and Roy Hargrove. JazzTimes ranked A Tale of God's Will sixth on its list of jazz albums with strings.