Frank Wright was born July 9, 1935, in Grenada, Mississippi, and grew up between Memphis and Cleveland, Ohio. In Cleveland he started out as a bass guitarist, backing touring rhythm-and-blues acts including Bobby "Blue" Bland and B.B. King, before switching to tenor saxophone after meeting fellow Clevelander Albert Ayler, whose example pulled him toward the horn. Cleveland also introduced him to pianist Bobby Few, who became his closest and longest-running musical partner. That circle's earliest surviving document is a pair of club dates recorded April 16 and 17, 1966, at La Cave in Cleveland, with Wright playing alongside Ayler, Ayler's trumpeter brother Donald Ayler, violinist Michel Samson, bassist Mutawef A. Shaheed and drummer Ronald Shannon Jackson; authorized by the Ayler estate, the tapes were finally issued in 2022 as La Cave Live, Cleveland 1966 Revisited.

Wright followed Ayler to New York, arriving in 1964. He sat in with John Coltrane's circle and, by most accounts, was invited to join the personnel for the June 1965 Ascension session but did not end up playing on it. ESP-Disk founder Bernard Stollman heard him sitting in with Coltrane and signed him on the spot; Wright cut his debut, Frank Wright Trio, on November 11, 1965, in New York with bassist Henry Grimes and drummer Tom Price, released the following year. A second ESP-Disk date, Your Prayer, followed on March 26, 1967, expanding to a quintet with alto saxophonist Arthur Jones, trumpeter Jacques Coursil, bassist Steve Tintweiss and drummer Muhammad Ali, the first time Wright and that drummer played together on record; both ESP albums were later combined, with a spoken interview, on the 2005 compilation The Complete ESP-Disk' Recordings.

In 1969 Wright relocated to Paris and formed the Frank Wright Quartet with alto saxophonist Noah Howard, Bobby Few on piano, and Muhammad Ali on drums. The group's debut, One for John (BYG Actuel, recorded December 5, 1969), was a tribute to Coltrane; Uhuru Na Umoja (America Records, recorded 1970 in Paris) used the same front line but, unusually, brought in drummer Art Taylor rather than Muhammad Ali for that one date, and Church Number Nine (recorded March 7, 1970, Paris) restored the regular Howard/Few/Ali lineup. Wright made a brief return to the United States in 1971 before settling back in France for good.

By the early 1970s, Wright and Few had founded their own Paris-based label, Center of the World Records, and renamed the working group Center of the World once bassist Alan Silva took over Noah Howard's chair. The band's founding record, Center of the World, Volume I, was recorded live March 26, 1972, at the Doelen in Rotterdam, with Wright, Few, Silva and Muhammad Ali; a Cadence critic later called it "revelatory" evidence of Wright's place among free jazz's founding generation. A second live date, Last Polka in Nancy? Volume 2, followed from the Nancy Jazz Pulsations festival on October 10, 1973, with the same quartet. Muhammad Ali and Wright also cut a duo record for the label, Adieu Little Man (recorded live at the American Center in Paris, April 1974), Ali's only outing as a credited co-leader. The label's catalog extended to several further volumes under the Center of the World imprint (including entries billed as More or Less Few, Inner Song, and two volumes of Solos & Duets), whose individual personnel were not independently confirmed in this build.

The later 1970s brought two Paris sessions credited to Sun Records: Shouting the Blues (recorded December 12, 1977) co-billed to Wright and pianist Georges Arvanitas, with bassist Jacky Samson and drummer Charles Saudrais; and Kevin, My Dear Son (recorded October 1978 at C.I. Recordings in New York, released 1979), a larger date reuniting Arvanitas with bassist Reggie Workman, drummer Philly Joe Jones, trumpeter Kamal Abdul Alim, percussionist Khalil Abdullah, and, singing on a piece co-composed by Wright and Few, vocalist Eddie Jefferson - the only time all three men shared a studio. That same year, the Frank Wright Sextet recorded Stove Man, Love Is the Word live at the Loft in Munich (May 22, 1979), and Wright appeared on the South African expatriate date Spiritual Knowledge and Grace (Ogun, recorded live June 22, 1979, in Eindhoven), co-billed with alto saxophonist Dudu Pukwana, bassist Johnny Dyani and drummer Louis Moholo.

Wright spent his last decade working mostly in Germany. He played in reedman Peter Brötzmann's group and in a trio led by the German painter and self-taught drummer A.R. Penck, documented on Run With the Cowboys (recorded in London, 1983) with bassist Peter Kowald. He also joined Cecil Taylor's large ensembles of the period, the Cecil Taylor Unit and the Orchestra of Two Continents, appearing on Winged Serpent (Sliding Quadrants) (Soul Note, 1985) and the later-issued Olu Iwa (Soul Note, 1994). Billed on Discogs under his own ordained title of "Reverend," Wright settled in Wuppertal, West Germany, where he passed away on May 17, 1990, at age 54. More than two decades later, in 2012, ESP-Disk issued a previously unheard live tape recorded July 17, 1974, at Ali's Alley in New York, the Soho loft club built and run by drummer Rashied Ali: released as Blues for Albert Ayler, it features Wright's quartet with guitarist James Blood Ulmer, bassist Benny Wilson, and, on drums, not Wright's regular collaborator Muhammad Ali but Muhammad's older brother, Rashied Ali himself, sitting in at his own venue.

Wright's tenor voice grew directly out of the "energy music" that Albert Ayler pioneered around him in Cleveland: a huge, vocalic tone, deliberate overblowing, and long, keening cries, though critics consistently noted that his phrasing stayed closer to the "earthier," gospel- and blues-inflected vocabulary of the rhythm-and-blues bands he had backed on bass guitar before he ever picked up a horn. He never recorded for a major label, working instead across a scattered run of small independents (ESP-Disk, BYG, America, his own Center of the World, Sun Records, Ogun, and later German independents), which kept his catalog undersized relative to his standing among contemporaries; a Cadence reviewer nonetheless placed him "in the pantheon of early free Jazz forefathers." His identity as an ordained minister, reflected in the "Reverend" honorific attached to his name on record labels and in Discogs' own artist records, fed directly into a playing style contemporaries described as preaching as much as performing. Later writers have traced his influence forward to younger free-tenor players including Glenn Spearman, Sabir Mateen, and Charles Gayle.