Paul E. West was born in Harlem on January 28, 1934, the son of a Lutheran minister, the Rev. Paul E. West, and a piano teacher. He started violin at six and studied with Albert Polnarioff, father of the violinist Paul Nero, until he was eighteen, winning the top award in a competition run by the National Guild of Violin Teachers. At the High School of Music and Art he served as student conductor of the senior symphony orchestra for his entire final year, led that orchestra in a concert for the visiting Philadelphia Orchestra conductor Eugene Ormandy, and between 1950 and 1953 built his own ensemble out of Harlem's churches and public schools, the Paul West Symphonic-Pop Orchestra and Chorus. He entered Wagner College on Staten Island in the autumn of 1954 on a basketball scholarship and switched from violin to bass that same year. During his freshman year he was playing four sets a night at the Baby Grand on 125th Street, riding the subway and the ferry back to campus at four in the morning to sleep in his brother's dormitory room.

His first recording was not a jazz date at all. On November 30, 1955 he played bass on Ray Charles's "Drown in My Own Tears" for Atlantic, in a band that included Cecil Payne on baritone saxophone and David "Panama" Francis on drums. Released in February 1956, it became Charles's third number one on the Billboard rhythm and blues chart. Jazz work followed almost immediately: in 1956 he cut six titles with the Charlie Rouse and Julius Watkins group that would soon be known as Les Jazz Modes, with Gildo Mahones on piano and Arthur Taylor on drums, issued on the Dawn label as one half of Jazzville '56.

In November 1956 he took the bass chair in Dizzy Gillespie's seventeen-piece orchestra, leaving Wagner to do it. The band's Birdland run of November 4 to December 2, 1956 was recorded and later issued, and West is on it alongside Lee Morgan, Al Grey, Melba Liston, Benny Golson, Billy Mitchell, Wynton Kelly and Charlie Persip. Over the following eight months that rhythm section made most of the Gillespie big band's Verve catalogue: the April 7 and 8, 1957 New York sessions that produced Birks' Works and filled out Dizzy in Greece, the April 17 quintet date with the violinist Stuff Smith and J.C. Heard, the Newport Jazz Festival set of July 6, 1957 that gave Verve two albums, and a July 8 studio session in New York. On February 18, 1957, while the band was on the West Coast, seven of its members booked a day at Master Recorders in Hollywood for Art Rupe's Specialty label and cut Dizzy Atmosphere under their own collective billing, with arrangements by Golson and Roger Hamilton Spotts. It is the one record in West's catalogue that carries his name on the front of the sleeve.

A year after leaving the Gillespie band he was back at Newport, on July 6, 1958, in the group Melba Liston assembled behind Dinah Washington: Kelly on piano, Max Roach on drums, Terry Gibbs and Don Elliott on vibraphone, Urbie Green and Liston on trombone, Blue Mitchell on trumpet, Sahib Shihab on baritone. EmArcy issued the set as Newport '58, and the same afternoon's festival is the one filmed for Jazz on a Summer's Day. The next fifteen years were freelance New York work of the kind that leaves a thin recorded trail and a thick working one: Billie Holiday, Carmen McRae, Betty Carter, Abbey Lincoln, Chris Connor, Joe Williams and Johnny Mathis among the singers, Lester Young, Milt Jackson, Jimmy Heath, George Coleman, Erroll Garner and Tommy Flanagan among the instrumentalists, plus touring with Petula Clark and Charles Aznavour and television dates on the David Frost Show, Soul, Positively Black and Like It Is. The vibraphonist Johnny Lytle's Close Enough for Jazz (Solid State, 1969) and Carmen McRae's Ms. Jazz (Groove Merchant, 1974), with Zoot Sims and Bucky Pizzarelli, are the recordings that survive from those years.

From January 1969 to September 1973 West was executive director of Jazzmobile, the Harlem organisation that puts jazz on flatbed trucks in the street. He produced 81 free summer concerts in 1969, 86 in 1970 and 96 in 1971, extended the operation to Baltimore, Washington, New Jersey, upstate New York and Westchester County, and ran lecture and demonstration concerts in schools across all five boroughs. In 1970 he conceived and built the Jazzmobile workshop, staffing it with thirteen instructors including Lee Morgan, Kenny Dorham, Jimmy Heath and Benny Powell; by 1973 it had roughly 300 students. Hiring Morgan to teach and to play was part of the trumpeter's recovery from addiction, and the friendship put West in the room at Slug's Saloon on the night of February 19, 1972, when Morgan was shot. He is one of the musicians who tell that story in Kasper Collin's 2016 documentary I Called Him Morgan.

He moved to the Henry Street Settlement Music School on the Lower East Side as its director in 1973 and stayed until April 2000, taking the student body from about 150 to roughly 700 and adding workshops in jazz, symphony orchestra, brass, strings, woodwinds, Latin music, choral singing and opera. The opera programme, begun in 1974, grew into a production group that staged a full work with orchestra and four casts every year, among them Lucia di Lammermoor, La Traviata, Madama Butterfly, Eugene Onegin and Carmen. He conducted the Henry Street Settlement Symphony Orchestra himself, including six annual tribute concerts to Dizzy Gillespie whose guest lists ran from Jon Faddis and Frank Wess to Roy Hargrove, Nicholas Payton, Claudio Roditi, Eddie Henderson, Jeremy Pelt and Diego Urcola, and a 1983 benefit at Avery Fisher Hall pairing Carmen McRae with his orchestra and Tony Bennett with the Count Basie band. The conducting became a recording credit in 1995, when Randy Weston brought him to Montreal to conduct the orchestra on Earth Birth, and he produced Weston's Zep Tepi in 2006. Playing never stopped: he was the bassist in Mike Longo's trio from 1993 through Only Time Will Tell in 2017, and recorded with Barry Harris, Roland Hanna, Junior Mance, Norman Simmons and Carol Sloane. In May 2022 he played a Jazz Foundation of America concert at the National Jazz Museum in Harlem in a trio with Kenny Barron and Willie Jones III, and on August 23, 2025 he conducted the Bethune Big Band, a band of retired swing-era musicians started by his brother Charles Lonny West, at the Blue Note in New York.

West is a timekeeper first, and the phrase he uses for the job is the one that explains his whole career: "You need to play the right notes, at the right time, to the right beat." Eighteen years of violin study before he ever touched a bass left him with an unusually exact ear for pitch, which is audible in the way he anchors the Gillespie band's Verve sides without ever crowding the ensemble, and it is the same training that let him step onto a podium in front of a symphony orchestra decades later. He belongs to the generation of New York bassists who learned the instrument inside big bands and then spent forty years accompanying singers, and the singers are the tell: Billie Holiday, Dinah Washington, Carmen McRae, Betty Carter, Joe Williams and Carol Sloane all hired him, which is a harder audition than any instrumental chair. Mike Longo, who played beside him for a quarter of a century, said he laid down the swinging-est grooves he knew. Randy Weston, who trusted him with an orchestra, said he had a wonderful touch as a conductor. West himself credits a churchgoing upbringing for keeping him clear of the addictions that took several of the musicians he came up with, and the practical steadiness that goes with that is the same quality both men were describing.