Houston Person was born on November 10, 1934, in Florence, South Carolina, and grew up there. He began on piano and switched to tenor saxophone as a teenager. He studied at South Carolina State College, which inducted him into its Hall of Fame in 1999. In the United States Air Force he joined a service band stationed in West Germany, where his bandmates included Don Ellis, Eddie Harris, Cedar Walton and Leo Wright, and afterward he continued his studies at the Hartt College of Music in Hartford, Connecticut.

By 1962 he was playing in the band of the organist Johnny "Hammond" Smith, and he can be heard on Smith's Mr. Wonderful (Riverside, 1963). The organ-combo circuit became his training ground. He recorded with the organists Don Patterson (Four Dimensions, recorded August 25, 1967, with guitarist Pat Martino) and Charles Earland (Black Talk!, December 15, 1969), and by most accounts it was in Smith's band that he met the singer Etta Jones. His own first album, Underground Soul!, was recorded for Prestige on June 16, 1966, at Rudy Van Gelder's studio in Englewood Cliffs, New Jersey, with the trombonist Mark Levine, the organist Charles Boston and the drummer Frankie Jones, and was produced by Cal Lampley.

Prestige issued eleven Person albums between 1966 and 1973, and they show how many settings the label tried for him. Chocomotive (June 14, 1967) and Trust in Me (October 13, 1967) put him in front of a piano rhythm section built around Cedar Walton, with Paul Chambers on bass for the second. Blue Odyssey (March 12, 1968) added the trombonist Curtis Fuller and the baritone saxophonist Pepper Adams. The organ-and-guitar dates came next: Soul Dance! (November 18, 1968), Goodness! (August 25, 1969, with organist Sonny Phillips and guitarist Billy Butler), Truth! (February 23, 1970) and Person to Person! (October 12, 1970, with guitarist Grant Green and drummer Idris Muhammad). Houston Express (April 8 and 9, 1971) used a horn section that included the trumpeter Thad Jones and arrangements by Horace Ott, and Broken Windows, Empty Hallways (May 1, 1972) and Sweet Buns & Barbeque (recorded September 11 and November 7, 1972) were arranged by Billy Ver Planck and Joe Beck. In the same years he was a sideman on Prestige dates for others, among them Earland's Black Talk!, Melvin Sparks's Sparks!, Charles Kynard's Afro-Disiac and, as a second tenor on one track, Gene Ammons's The Boss Is Back! (November 10 and 11, 1969).

After Prestige he made the double live album The Real Thing, recorded March 14 and 15, 1973, at Watt's Club Mozambique in Detroit and issued on Eastbound, with Green, Phillips and, on some tracks, the Motown bassist James Jamerson. Westbound followed in 1975 with Houston Person '75 and Get Out'a My Way!, Mercury in 1976 and 1977 with Pure Pleasure and Harmony, and then a long run for Muse that began with Stolen Sweets (recorded 1976) and included The Big Horn, Wild Flower, The Nearness of You, Suspicions, Heavy Juice and The Talk of the Town. Savoy issued The Gospel Soul of Houston Person in 1978. In the 1980s he recorded Road Warriors (Greene Street, 1984) with Les McCann and Creation (1984) with the pianist Roger Kellaway.

The central partnership of his career was with Etta Jones. They were billed as equals and worked together for years, touring and recording, and many people assumed they were married, which they were not. From the mid-1970s Person also produced and managed her. He plays on Etta Jones '75 (Westbound) and on most of her albums for Muse and then HighNote, beginning with Ms. Jones to You (Muse, 1976), and produced many of them. Their last album, Etta Jones Sings Lady Day, was recorded on June 21, 2001, and Jones passed away on October 16, 2001. Person's production work extended well beyond her: he produced Antoine Roney's Whirling (1996) and the pianist Richard Wyands's As Long As There's Music (2001), among many other dates for Muse and its successor label.

Duets with the bassist Ron Carter became a second thread. Something in Common (recorded February 23, 1989) and Now's the Time (January 6, 1990) were followed by Dialogues (August 18, 2000), Just Between Friends (October 26, 2005), Chemistry (December 22, 2015) and Remember Love (March 27, 2018), six saxophone-and-bass albums in all. He also made a saxophone-and-piano duo album, You Taught My Heart to Sing, with Bill Charlap (recorded August 4, 2004; released 2006). Since 1997 his own records have appeared mostly on HighNote, the successor to Muse, starting with Close Encounters (recorded November 6, 1996, with the tenor saxophonist Teddy Edwards) and Person-ified (November 26, 1996, released March 4, 1997, with Wyands, bassist Ray Drummond and drummer Kenny Washington). Most of those sessions were made at Van Gelder Studio, and the 2022 album Reminiscing at Rudy's, recorded there in a single day on July 19, 2022, was his tribute to the late engineer. Over the same years he played on Lena Horne's Blue Note albums of the 1990s and on the organist Joey DeFrancesco's All About My Girl (Muse, 1994).

Person has more than 75 albums as a leader. His honors include the Eubie Blake Jazz Award (1982) and a Jazz Legend Award presented in San Diego in 2011, along with the South Carolina State Hall of Fame induction. In recent years he has recorded with Emmet Cohen for the pianist's Masters Legacy Series (Volume 5, recorded May 16, 2023, at Van Gelder Studio and released November 10, 2023), with the bassist John Clayton on Family Tree (2023), and with the pianist Joe Alterman on Brisket for Breakfast (2025). A livestreamed concert celebrating his 90th birthday paired him with the alto and soprano saxophonist Eric Person, who is not related to him.

Person plays tenor in the big, warm, blues-rooted sound of the soul-jazz and "boss tenor" tradition, a line that runs through Gene Ammons and Eddie "Lockjaw" Davis, both of whom his tone is often compared with. He has also cited Earl Bostic, Illinois Jacquet, Lester Young, Arnett Cobb and Charlie Parker. He is best known for soul jazz, but he has moved between organ-guitar funk dates, hard bop quintets, swing and standards, and his later records lean on ballads, the blues and the Great American Songbook, played at medium tempos with a patient melodic focus. He is also one of the well-known accompanists to singers: his partnership with Etta Jones, in which his horn answered her phrases and left her space, shaped both of their catalogs, and he has also recorded with Lena Horne, Lou Rawls, Charles Brown, Dakota Staton and Janis Siegel. In the late 1960s and early 1970s he was part of the same groove-oriented circle as Grant Green, Stanley Turrentine, Charles Earland and Richard "Groove" Holmes.