Branford Marsalis was born on August 26, 1960, in Breaux Bridge, Louisiana, the eldest son of the pianist and educator Ellis Marsalis Jr. and the singer and teacher Dolores Ferdinand Marsalis. His brothers Wynton Marsalis, Delfeayo and Jason also became jazz musicians. He grew up in the New Orleans area and attended the New Orleans Center for Creative Arts, starting on piano and clarinet before settling on saxophone in his mid-teens. In high school he played in an R&B cover band called the Creators. At Southern University in Baton Rouge he studied with the clarinetist Alvin Batiste, who encouraged him to transfer to the Berklee College of Music in Boston.

While still a Berklee student he toured Europe on alto and tenor saxophone in a big band led by the drummer Art Blakey, and over the following year he also worked in big bands led by Lionel Hampton and Clark Terry. By the end of 1981 he was playing alto in Blakey's Jazz Messengers alongside his brother Wynton. Concerts with Wynton, including a 1981 tour of Japan with Herbie Hancock, led to Wynton's first quintet, where Branford moved to soprano and tenor and stayed until 1985. He is heard on that group's Columbia albums Think of One (1983), Hot House Flowers (1984) and Black Codes (From the Underground) (1985), and he made his own debut, Scenes in the City, for Columbia in 1984. In the same years he appeared on records by Miles Davis and Dizzy Gillespie.

In 1985 he left the quintet to join the former Police singer Sting's first solo band, which recorded The Dream of the Blue Turtles with Kenny Kirkland on keyboards, Omar Hakim on drums and Darryl Jones on bass, and played the London Live Aid concert on July 13, 1985. He remained a regular in Sting's studio and live lineups until Brand New Day (1999). In 1986 he formed the Branford Marsalis Quartet with Kirkland, the drummer Jeff "Tain" Watts and the bassist Robert Hurst, while his own Royal Garden Blues (1986) was recorded with several different rhythm sections. That group's later records include Crazy People Music (1990) and I Heard You Twice the First Time (1992), a set of blues explorations with guests that included his brother Wynton, B.B. King and John Lee Hooker, which won the Grammy for best jazz instrumental performance, individual or group. He acted in and played on Spike Lee's School Daze (1988), opened Do the Right Thing (1989) with a solo of "Lift Every Voice and Sing," and led the quartet on the soundtrack of Mo' Better Blues (1990), with Terence Blanchard featured on trumpet. He also recorded with Public Enemy ("Fight the Power") and sat in repeatedly with the Grateful Dead, appearing on their 1990 live album Without a Net.

From 1992 to 1995 he led The Tonight Show Band on The Tonight Show with Jay Leno, bringing three members of his quartet with him, and he left the job in 1995, handing the band to the guitarist Kevin Eubanks. In 1994 he formed Buckshot LeFonque, a jazz group drawing on rock and hip-hop and named for a pseudonym once used by Cannonball Adderley, and shared a Grammy for best pop instrumental performance with the pianist and singer Bruce Hornsby for "Barcelona Mona." Eric Revis replaced Hurst in the quartet in 1997. Kirkland died in November 1998, and Requiem (1999) became his last recording with the group; Joey Calderazzo took the piano chair, and Contemporary Jazz (2000), their first album together, won Marsalis another Grammy at the 2001 ceremony. In 2002 he founded his own label, Marsalis Music, which issued his quartet albums Footsteps of Our Fathers (2002, built around John Coltrane's A Love Supreme and Sonny Rollins's The Freedom Suite), Romare Bearden Revealed (2003), Eternal (2004), Braggtown (2006) and Metamorphosen (2009), and records by artists including Miguel Zenón, Claudia Acuña and the guitarist Doug Wamble. He taught at Michigan State University from 1996 to 2000 and at San Francisco State University from 2000 to 2002, and North Carolina Central University's jazz studies program lists him as one of its artists-in-residence.

After Hurricane Katrina in 2005 he and Harry Connick Jr. worked with Habitat for Humanity to create Musicians' Village in New Orleans' Upper Ninth Ward; its centerpiece, the Ellis Marsalis Center for Music, opened in August 2011, and in January 2024 he became its artistic director, a post his father had held. Jeff Watts left the quartet in 2009 and was replaced by the drummer Justin Faulkner, who is on Four MFs Playin' Tunes (2012). Marsalis and Calderazzo made the duo album Songs of Mirth and Melancholy (2011), he released the solo recital In My Solitude: Live at Grace Cathedral (2014), and the quartet recorded Upward Spiral (2016) with the singer Kurt Elling, which was nominated for the Grammy for best jazz vocal album. The Secret Between the Shadow and the Soul, recorded at Monash University in Melbourne in May 2018 and released in 2019, was nominated for best jazz instrumental album. Alongside the quartet he is a frequent classical soloist, with the Orpheus Chamber Orchestra (Creation, 2001), the North Carolina Symphony (American Spectrum, 2009) and the New York Philharmonic (2010), among others. He wrote the music for the Broadway revivals of Fences (2010, a Tony nomination and a Drama Desk Award) and Children of a Lesser God (2018) and for the new play The Mountaintop (2011), arranged and orchestrated A Wonderful World: The Louis Armstrong Musical (2024), and scored the films Ma Rainey's Black Bottom (2020) and Rustin (2023) and the documentary Tulsa Burning (an Emmy nomination in 2021).

For Belonging, released on March 28, 2025, the quartet moved to Blue Note, recording a full-album reading of Keith Jarrett's 1974 album of the same name in March 2024 at the Ellis Marsalis Center for Music; it was nominated for best jazz instrumental album at the 2026 Grammys. His second Blue Note album, Dedicated to You, pairs the quartet with Dianne Reeves in a tribute to John Coltrane in his centennial year, built around the 1963 album John Coltrane and Johnny Hartman, and was released on September 18, 2026. Tour dates for the album begin in Europe in November 2026 and continue in North America in early 2027. Marsalis has won three Grammy Awards, for I Heard You Twice the First Time (1993), "Barcelona Mona" (1994) and Contemporary Jazz (2001). The Marsalis family, with Ellis, Wynton, Delfeayo and Jason, received the NEA Jazz Masters award in 2011, the first time the honor went to a family, and he received the North Carolina Award in 2011 and an honorary doctorate from Berklee in 2006. He was named Wake Forest University's Maya Angelou Artist-in-Residence for 2025.

Marsalis plays mostly tenor and soprano saxophone in jazz, and has played alto less often since the late 1980s, though he uses it in classical concertos. His tenor work is full-bodied and harmonically sophisticated, rooted in the modal and post-bop language of Wayne Shorter and John Coltrane, with Sonny Rollins also named by AllMusic among his early comparisons. His quartet is known for its unusually stable personnel and a deep book of originals by himself, Calderazzo and Revis, alongside standards and reinterpretations: Footsteps of Our Fathers (2002) takes up A Love Supreme and The Freedom Suite, Belonging (2025) follows the parts that Jan Garbarek played on Keith Jarrett's 1974 record, and Metamorphosen (2009) honored mentors and friends who had died, among them Alvin Batiste, Michael Brecker and Freddie Hubbard. He has moved easily between idioms, from Sting's pop-jazz band and the Grateful Dead to hip-hop with Buckshot LeFonque and orchestral concertos by Glazunov, Villa-Lobos and John Adams, and AllMusic calls him a musical chameleon. He has said that the quartet's long familiarity lets it play adventurous, sophisticated music without playing defensively. His early-1980s emergence alongside his brother Wynton Marsalis belonged to the young-lions movement that brought acoustic post-bop back to the mainstream.