William Reese Perkins was born July 22, 1924, in San Francisco, but spent his early childhood in Chile, where his father worked as a mining engineer. He started on clarinet and switched to tenor saxophone at fifteen; after his father's death in his teens, his mother raised him in Santa Barbara. Perkins's path to music ran through engineering rather than a conservatory: he studied electrical engineering at Caltech, earned his degree, served in the Navy at the end of World War II, then used the GI Bill to take a music degree at UC Santa Barbara. His first professional gig came comparatively late, in 1950, joining bandleader Jerry Wald's Los Angeles orchestra at twenty-six.

In May 1951 he joined Woody Herman's Third Herd, reportedly recruited mid-engagement to replace a tenor player who had just been fired. His light, floating tone in the Lester Young mold fit naturally alongside Herman's other "Prez" disciples, and he can be heard on the band's recording of "Ill Wind." In 1953 he moved, together with fellow tenor Richie Kamuca, into Stan Kenton's orchestra, where "Yesterdays" became one of his signature features; he rejoined Herman briefly in 1954 before further stints with Kenton later in the decade. These big-band years put him at the center of the Los Angeles studio and jam-session circuit that produced West Coast jazz: he worked with Shorty Rogers's Giants, pianist John Lewis, altoist Art Pepper, Terry Gibbs's Dream Band, and Howard Rumsey's Lighthouse All-Stars at the Lighthouse Cafe in Hermosa Beach.

On February 10, 1956, Perkins recorded Grand Encounter: 2° East - 3° West for Pacific Jazz alongside John Lewis, Percy Heath, Jim Hall, and Chico Hamilton, a session pairing the East Coast's Modern Jazz Quartet pianist with West Coast players that has become one of the era's most admired small-group cool-jazz dates. The same year brought his first outing billed as a leader, On Stage (Pacific Jazz), an octet session with Bud Shank, Stu Williamson, Carl Fontana, Russ Freeman, Jack Nimitz, Red Mitchell, and Mel Lewis, and The Brothers! (RCA Victor), reuniting him with Al Cohn and Richie Kamuca as a three-tenor front line tracing back to the "Four Brothers" sax-section lineage that ran through Herman's own bands. He and Kamuca continued as a pair on Tenors Head-On (1957, Liberty) and were joined by Art Pepper on Just Friends (1957, Pacific Jazz).

Through the 1960s, as jazz work in Los Angeles thinned, Perkins built a parallel career as a recording engineer while continuing to record as a leader, including the Latin-jazz date Mucho Calor (1958) and Bossa Nova With Strings Attached (1963, Liberty). Unlike many West Coast contemporaries who stayed inside the cool-jazz vocabulary they had established in the 1950s, he kept absorbing newer influences, and by the late 1960s his tenor playing showed the reach of Sonny Rollins. In November 1966 he recorded what is often cited as his finest album, Quietly There (Riverside, released 1970), a quintet date built around Johnny Mandel compositions with vibraphonist/pianist Victor Feldman. In 1969 he moved into studio work full-time, and from 1970 to 1992 he held a chair in Doc Severinsen's Tonight Show band.

That studio decade also brought his most historically notable big-band association after Kenton and Herman: from 1974 to 1977 he played baritone saxophone in the Toshiko Akiyoshi-Lew Tabackin Big Band, one of a rotating cast of West Coast studio players (alongside Gary Foster, Dick Spencer, Bobby Shew, Peter Donald, and Don Baldwin) who filled out the band's book on record. He is on the baritone chair for Kogun (1974), Long Yellow Road (1975), Insights (1976), Tales of a Courtesan (Oirantan) (1975/1976), and March of the Tadpoles (1977) - the stretch of albums that earned Akiyoshi three Grammy nominations and a Down Beat critics' poll win. Through the same years he also worked with Bill Holman's band and rejoined Herman for occasional reunion projects. His own leader dates from this period and after, mostly for small independent labels (Interplay, Fresh Sound, Sea Breeze, Jazz Mark), include Confluence (1979, with baritone counterpart Pepper Adams), Many Ways to Go (1980), Journey to the East (recorded 1984, released 1985, Contemporary, with drummer Peter Donald from the Akiyoshi band), The Right Chemistry (recorded 1987, released 1989, with tenor saxophonist James Clay), Killer Joe (recorded 1987 in Barcelona, released 1988), Peaceful Moments (1989, also cut in Barcelona), Two Brothers (recorded 1989, released 1992, with trombonist Herbie Harper), Warm Moods (recorded 1991, released 1992, with pianist Frank Strazzeri), the Woody Herman tribute Our Man Woody (1991, billed to the Bill Perkins Big Band), Frame of Mind (1994), Live at Capozolli's (recorded 1997, released 1998, with trumpeter Steve Huffsteter), and Perk Plays Prez (recorded 1995, released 1996, Fresh Sound), a tribute to his first idol Lester Young cut with the Jan Lundgren Trio.

Perkins also returned to the Lighthouse All-Stars when Shorty Rogers revived the group in the 1980s and 1990s, switching from baritone back to tenor after saxophonist Bob Cooper's death in 1993. He was diagnosed with cancer in the early 1990s, ultimately affecting his lungs, hip, and throat, and underwent multiple throat surgeries over the following decade, but kept performing and teaching workshops internationally between treatments. He continued to play with Bill Holman's band into 2003 and died of cancer at his Sherman Oaks home on August 9, 2003, at age seventy-nine.

Perkins's foundation was Lester Young's light, vibrato-light "Prez tone," the same sound that made him fit naturally among Woody Herman's other Young-influenced tenors in the early 1950s and that placed him squarely inside the cool, West Coast school built alongside contemporaries such as Richie Kamuca, Al Cohn, and Bud Shank. What set him apart within that circle was a restlessness about staying there: from the late 1960s on he absorbed Sonny Rollins's harmonic reach on tenor and, later, John Coltrane's influence on soprano saxophone, at a time when many of his West Coast peers kept working the vocabulary they had already mastered. He was also an unusually complete "doubler" even by the standards of a working session player, moving between tenor, baritone, clarinet, bass clarinet, and flute across his leader and sideman dates, including a stretch on baritone in Toshiko Akiyoshi's big band. His parallel career as a recording engineer, built on an electrical-engineering degree earned before he ever finished a music degree, is unusual among prominent West Coast horn players of his generation and points to the same technical bent that made him a first-call Los Angeles studio musician for decades.