Anthony Claiborne Jackson was born in New York City on June 23, 1952, and grew up in Manhattan. He began on piano, moved to guitar as a teenager, and settled on bass after hearing James Jamerson on Motown records and Jack Casady in rock. His teachers included Jerry Fisher, Lawrence Lucie and the guitarist Pat Martino. DownBeat's memorial notice has him playing local clubs by sixteen, and AllMusic says he was working as a session player at eighteen.

His first breakthrough came out of Philadelphia. Around 1972 he joined the band of the singer Billy Paul and began working for Gamble and Huff's Philadelphia International label; Paul's "Me and Mrs. Jones" (1972) was the first number one record he played on. In the fall of 1973 he was in the rhythm section, drawn from the MFSB house band, that rehearsed and cut "For the Love of Money" for The O'Jays' album Ship Ahoy. The engineer Joe Tarsia noticed the wah-wah pedal attached to Jackson's Fender Precision bass, ran the signal through a phaser and later added echo, and the opening riff became one of the best-known bass figures in popular music. The single reached No. 9 on the pop chart and No. 3 on the R&B chart in 1974, and the writing credit lists Jackson alongside Kenny Gamble and Leon Huff.

He was already working on a second idea. Frustrated by the limited range of the four-string bass, he approached luthiers in 1974 about a six-string "contrabass guitar" tuned in fourths from a low B to a high C, and Carl Thompson built the first one for him in 1975. He first performed on it that year, recording with the saxophonist Carlos Garnett and touring with Roberta Flack, and he plays on her album Feel Like Makin' Love (1975). From 1982 he played the contrabass guitar almost exclusively. Fodera introduced the Anthony Jackson Signature Model in 1984 and the single-cutaway Presentation model in 1989, and he is credited with developing the modern six-string bass.

New York's studios and touring bands kept him busy through the late 1970s and 1980s. He played on the drummer Buddy Rich's mid-1970s Groove Merchant albums, on the 1976 Kudu sessions of Hank Crawford, Esther Phillips and Grover Washington Jr., and on Chick Corea's The Leprechaun (1976). From 1976 to 1982 he was the bassist on Al Di Meola's Columbia albums, from Land of the Midnight Sun through Elegant Gypsy, Casino, Splendido Hotel and Electric Rendezvous, and on the live Tour de Force, a band that also included Steve Gadd and Jan Hammer. He recorded Patti Austin's Havana Candy (1977) and Every Home Should Have One (1981), Quincy Jones's Sounds...And Stuff Like That!! (1978), Chaka Khan's Chaka (1978) and five later albums, and three Columbia albums with the guitarist Eric Gale. He is on Paul Simon's One-Trick Pony (1980), played in the band for Simon and Garfunkel's 1981 Central Park concert, and appears on two tracks each of Steely Dan's Gaucho (1980) and Donald Fagen's The Nightfly (1982). Alongside the American work came Japanese sessions for Jun Fukamachi, Terumasa Hino, Sadao Watanabe and others.

From the mid-1980s his most durable jazz partnerships were with pianists. The trio of the pianist Michel Camilo, with Jackson on contrabass guitar and the drummer Cliff Almond, was Camilo's regular group for many years, and Jackson plays on Camilo's debut Why Not? (1985) and on records through Caribe (2009). With the guitarist Steve Khan he made Eyewitness (1981) and a run of albums through Crossings (1994), and Khan, Jackson and the drummer Dennis Chambers worked as a trio recorded live in Cologne in 1994 (The Suitcase: Live in Köln '94, released 2008) and again in 2010 (Parting Shot, 2011). He played on Michel Petrucciani's Music (1989), Playground (1991) and Both Worlds (1997), and joined Petrucciani and Gadd for the 1997 trio tour captured on Trio in Tokyo. He also recorded with Mike Stern, Dave Weckl, Tania Maria, Lee Ritenour and Earl Klugh.

His last major band was the pianist Hiromi Uehara's. He was a guest bassist on three tracks of her debut Another Mind (2003), played on three tracks of Brain (2004), and from 2011 to 2016 was the bassist in her Trio Project with the drummer Simon Phillips, which made Voice (2011), Move (2012), Alive (2014) and Spark (2016) for Telarc. In 2010 he co-led the album Interspirit with the bassist Yiorgos Fakanas for Abstract Logix; its liner notes credit him with more than 3,000 sessions on more than 500 albums and live performances in more than 30 countries.

Illness forced him to miss some Trio Project concerts in 2016, and his health kept him from performing after 2017. A benefit concert, "For the Love of Anthony," was held at Shapeshifter Lab in Brooklyn in February 2025, with bassists including Ron Carter, Victor Wooten, Christian McBride and Stanley Clarke in attendance. He passed away on October 19, 2025, on Staten Island, at the age of 73. He had Parkinson's disease. Hiromi is reviving the Trio Project name for a fall 2026 tour and recording, with Phillips back on drums and James Genus on bass.

Jackson was a bassist who treated the instrument as a subject of study. AllMusic calls him an academician whose research into the origins of the bass led to the six-string contrabass guitar, and he argued in a 1990 Bass Player interview that because the bass is the lowest-pitched member of the guitar family, six strings were the logical design from the start and not a novelty. The low B string gave him notes that four-string players reached only by detuning, and the high C string let him play melodies and chords above the usual range. Leaders of technically demanding fusion and piano-trio music kept hiring him over several decades, among them Al Di Meola, Michel Camilo, Michel Petrucciani, Steve Khan and Hiromi Uehara.

His own influences were James Jamerson, whom he later helped honor with a contribution to Allan Slutsky's book and CD set on Jamerson's work, and Jack Casady. The picked, phase-shifted line on "For the Love of Money" set a precedent among four-string players, AllMusic notes, and Consequence ranked him No. 43 on its list of the 100 greatest bassists. He belongs in a crossover catalog because his career ran as much through R&B, soul and pop sessions as through jazz: the same player appears on Chaka Khan, Paul Simon and Roberta Flack records and anchored the Camilo and Hiromi trios.