Elizabeth LaCharla Wright was born on January 22, 1980, in Hahira, Georgia, the middle of three children of two ministers. She served as musical director of the small church where her father was pastor, and call and response with the congregation was her first music. The household was strictly Pentecostal, with little television and limited radio, and she sang gospel with her brother and sister and played piano at church. She first heard jazz on pianist Marian McPartland's National Public Radio program. After Houston County High School in Warner Robins, where she received a National Choral Award, she enrolled at Georgia State University in Atlanta to study voice but left before finishing. A jam session at the Atlanta Jazz Festival in 1999 brought her to notice, and a fan, Ron Simblist, introduced her to the Atlanta vocal group In the Spirit, which she joined in 2000 and sang with until 2002. Simblist also sent her demos to Ron Goldstein, president of Verve Music Group. In 2002 she sang on touring Billie Holiday tribute concerts in Los Angeles and Chicago, on bills that included Lou Rawls and Dianne Reeves, which made her name nationally, and Verve signed her that year.

Her debut, Salt (Verve, 2003), began with sessions in 2002 under the bassist and arranger John Clayton that were scrapped; Tommy LiPuma took over, sharing production credit with drummer Brian Blade and pianist Jon Cowherd. Cowherd, Blade, keyboardist Kenny Banks, guitarist John Hart, bassist Doug Weiss and percussionist Jeff Haynes formed the core band, with guests including Danilo Pérez on "Afro Blue," Chris Potter on soprano saxophone, Myron Walden on alto saxophone and bass clarinet, and Sam Yahel on organ. Wright wrote four of the twelve tracks ("Salt," "Eternity," "Fire," "Silence"), co-wrote "Blue Rose" with Banks, and also recorded Chick Corea's "Open Your Eyes, You Can Fly," the traditional "Walk with Me, Lord" and Gordon Jenkins's "Goodbye." The album reached No. 2 on Billboard's Top Contemporary Jazz chart and No. 4 on its Top Jazz Albums chart, critics compared her to Norah Jones and Cassandra Wilson, and JazzTimes readers named her best new artist. She also sang on two tracks of Joe Sample's The Pecan Tree (2002), took part in Danilo Pérez's ...Till Then (Verve, 2003), and toured as an opening act for Ray Charles.

Dreaming Wide Awake (Verve Forecast, June 14, 2005) moved toward a folk, pop and soul blend. Producer Craig Street recorded the band playing together in one room at Allaire Studios in the Catskills, with guitarists Chris Bruce, Bill Frisell and Greg Leisz, bassist David Piltch and drummer Earl Harvin, and the repertoire included Neil Young's "Old Man" and Joe Henry's "Stop." It reached No. 1 on the Top Contemporary Jazz chart in 2005 and 2006, and its "Hit the Ground" was used in an episode of the television series House. Street produced The Orchard (Verve Forecast, February 2008) as well, bringing in Joey Burns and John Convertino of Calexico and the singer-guitarist Toshi Reagon for a set that included Ike Turner's "I Idolize You" and Led Zeppelin's "Thank You"; German sources report that both albums reached the top three of the US jazz charts. In those years she also guested for others: on David Sanborn's Closer (2005), on Toots Thielemans's One More for the Road (2006), in a duet of "Whispering Pines" with Jakob Dylan for the 2007 Band tribute Endless Highway, with Regina Carter and Russell Malone on "Reaching for the Moon" for the 2007 Ella Fitzgerald tribute We All Love Ella, and on Massimo Biolcati's Persona (2008).

Fellowship (Verve Forecast, September 28, 2010) turned to gospel standards and spirituals, with guests including Meshell Ndegeocello, Bernice Johnson Reagon, Joan as Policewoman and Angélique Kidjo, and debuted at No. 2 on Billboard's jazz albums chart. She sang at JazzFest Berlin in 2011, and in 2013 she was the vocalist on "Backward Country Boy Blues" on Terri Lyne Carrington's Money Jungle: Provocative in Blue, a reworking of the 1962 Duke Ellington, Charles Mingus and Max Roach trio album that won the 2013 Grammy Award for Best Jazz Instrumental Album. Freedom & Surrender (Concord, September 4, 2015) was produced by Larry Klein with guitarist Dean Parks and drummer Vinnie Colaiuta. Most of its songs were written by Wright with Klein and David Batteau, and it included a duet with Gregory Porter on "Right Where You Are," Nick Drake's "River Man" with Till Brönner on flugelhorn, and Billy Childs on Fender Rhodes on one track. Its single "Lean In" was included on President Obama's summer 2016 playlist. In 2015 she also co-wrote "This Song in Me" with Derrick Hodge for Kendrick Scott Oracle's We Are the Drum. On October 22, 2016 she was one of the singers with the Count Basie Orchestra at the Apollo Theater for the centennial of Ella Fitzgerald's birth, a concert later released by Concord Jazz as Ella 100: Live at the Apollo!.

Grace (Concord, September 15, 2017) was produced by Joe Henry. Wright sang with drummer Jay Bellerose, bassist David Piltch, guitarists Chris Bruce and Marvin Sewell, and Banks on piano and Hammond organ, with Marc Ribot guesting on one track and an Atlanta church choir directed by Kenny Banks Sr. on three. Its songs drew on Allen Toussaint ("Southern Nights"), Nina Simone ("Seems I'm Never Tired of Lovin' You"), Bob Dylan ("Every Grain of Sand"), k.d. lang ("Wash Me Clean") and Sister Rosetta Tharpe ("Singing in My Soul"). She also appeared on Taj Mahal and Keb' Mo's TajMo (Concord, 2017), and joined Angélique Kidjo and Cécile McLorin Salvant in Carrington's Sing the Truth project, in which the singers perform songs associated with women such as Odetta, Billie Holiday and Miriam Makeba; they appeared together at the Rudolstadt Festival in Germany on July 4, 2019.

In 2022 she launched her own label, Blues & Greens Records, with Holding Space (Live in Berlin) (June 15, 2022), a concert recorded in 2018 at Berlin's Columbia Theater with Chris Bruce on guitar, Bobby Ray Sparks II on keyboards, Ben Zwerin on bass and Ivan Edwards on drums. Shadow (April 12, 2024), her first studio album since Grace, was produced by Bruce, with Angélique Kidjo and Ndegeocello as guests, original songs including "Sparrow," and covers of songs by Cole Porter, Sandy Denny and Gillian Welch; Stereophile gave it four and a half stars for performance. Nearness (Blues & Greens and Candid, September 25, 2026) is a duo album of eleven standards and spirituals with Kenny Banks Sr. on piano and organ, again produced by Bruce, and she began touring it in October 2026 with United States and European dates announced into 2027. She played the San Javier Jazz Festival in Spain in July 2026 with guitarist Adam Levy, bassist Kyle Miles and drummer Marlon Patton.

Wright is a dark-toned alto whose sound grows from church music: Pentecostal gospel, call and response and congregational singing came first, and jazz and blues arrived later through radio and the Atlanta scene. DownBeat's reviewer wrote that she approaches her music with equal parts gospel, jazz, R&B and blues, and Stereophile praised a voice of richness and clarity with an impression of great power held in reserve. Her choice of material is deliberately wide, spanning Chick Corea, Neil Young, Led Zeppelin, Nick Drake, the Bee Gees, Gillian Welch and Cole Porter alongside her own songs and spirituals, and she has said that Shadow was the record she always wanted to make, free of label pressure toward a single genre, bringing Americana into her jazz. She sits between jazz, gospel and soul rather than inside one tradition, but she is a jazz singer by label history (Verve and Concord, Billboard jazz chart positions on every album from Salt to Fellowship), by the jazz festivals and jazz press that book and review her, and by her work with Terri Lyne Carrington, Danilo Pérez and Toots Thielemans, even as Stereophile noted she has never quite reached major status as a jazz singer. Early reviewers likened her to Norah Jones and Cassandra Wilson, and her tribute work with the Count Basie Orchestra and in Sing the Truth places her in the line of Ella Fitzgerald, Billie Holiday and Nina Simone.