Roger Kellaway was born on November 1, 1939, in Waban, a village of Newton, Massachusetts. He has described it as a town with one policeman, one drugstore, one bank and one market, where the trains were still pulled by steam. Formal piano lessons began at seven. At eleven he bought the sheet music to George Shearing's "I'll Remember April" and kept it as his solo piece for years; after Shearing he listened to Billy Taylor, Oscar Peterson and Horace Silver, on top of a listening diet that was still mostly classical. In junior high school eight children auditioned for the orchestra's piano chair, so he taught himself the upright bass instead, and four years later played fourth bass in the Massachusetts All-State Orchestra under Frederick Fennell. At Newton High School he took college-level theory and played double bass and percussion in the orchestra, and on the side played jazz bass in a local band called the King's Men alongside the cornetist Dick Sudhalter, who pushed him toward Dixieland while a tenor player named Dave Schreier pushed him toward modern jazz.

He entered the New England Conservatory in 1957 and studied piano, double bass and composition there for two years. The formative figures were not faculty but two multi-instrumentalists he played with, Dick Wetmore and Leroy "Sam" Parkins. With Wetmore he worked the basement of Boston's Hotel Buckminster on a mixture of Dixieland and modern jazz, and every other Sunday accompanied readings of E. E. Cummings with improvisations built on Wetmore's twelve-tone rows. With Parkins he took a Dixieland job on Cape Cod where the drummer was Tommy Benford, a veteran of two world tours with Fats Waller. He left the Conservatory in 1959 to play bass with Jimmy McPartland, and by the time he reached New York in 1960 he was still primarily a bassist. He sat in on bass with Jimmy Giuffre and Jim Hall, and Giuffre offered him the gig, which personal circumstances made him turn down. Giuffre's next trio took Steve Swallow instead. Kellaway then switched to piano for good.

The New York years came fast. He plays piano on Mark Murphy's That's How I Love the Blues (Riverside, 1963), a date conducted and arranged by Al Cohn with Jim Hall on guitar, Clark Terry and Snooky Young on trumpets and Dick Hyman on organ; Kellaway himself dates the session to 1962. That same year he wrote every arrangement for the Clark Terry Sextet's More (Theme from Mondo Cane) on Cameo, with Ben Webster on tenor. Between 1963 and 1965 he worked with Kai Winding, with Cohn and Zoot Sims, and for roughly two and a half years with the Clark Terry and Bob Brookmeyer Quintet, whose Mainstream albums Tonight and The Power of Positive Swinging both appeared in 1965 with Bill Crow and Dave Bailey completing the rhythm section. The sideman credits from those three years are the ones listeners still know him by: Oliver Nelson's More Blues and the Abstract Truth, cut over two days in November 1964 with Pepper Adams, Phil Woods, Thad Jones and Ben Webster; Webster's own See You at the Fair (1964), where he plays half the album and was made to use an electric harpsichord on two tracks he still dislikes; Wes Montgomery's Bumpin', rehearsed for four days in May 1965 under Don Sebesky's supervision because Montgomery did not read music; Kenny Burrell's Guitar Forms, where his piano is confined to three tracks of Gil Evans's orchestration; and Sonny Rollins's Alfie (1966), on which he took a second solo in the middle of "Transition Theme" after Rollins stepped away from the microphone. He also spent a stretch at the Half Note subbing for Wynton Kelly in Montgomery's group with Paul Chambers on bass, the only time the two played together. His own first records came in parallel: a Regina LP with Jim Hall in 1963 and The Roger Kellaway Trio for Prestige in 1965.

In 1966 he moved to Los Angeles, played in Don Ellis's orchestra, and moved into studio and screen work without leaving the jazz side of his catalog behind. A year as musical director for the comedian Jack E. Leonard led, on drummer Stan Levey's recommendation, to the same job with Bobby Darin from 1967. Darin handed him Leslie Bricusse's songs from Doctor Dolittle, named a studio and a 35-piece orchestra, and gave him three weeks; the resulting Bobby Darin Sings Doctor Dolittle (Atlantic, 1967) is an album Kellaway still names among his proudest work. His own Stride! and Spirit Feel, the latter a quartet with Tom Scott, Chuck Domanico and John Guerin, both appeared in 1967. Arranging work followed for Melanie, Carmen McRae, Liza Minnelli, Diane Schuur and Robben Ford, who has named Kellaway and Tom Scott as the two major influences on his music. Kellaway produced McRae's I Am Music (Blue Note, 1975) outright, arranged and conducted most of it, and put his own "I Have the Feeling I've Been Here Before," with lyrics by Alan and Marilyn Bergman, at its center.

The record that changed his standing was built in his own living room. In 1969 he was writing pieces for cello and piano and asked his favourite studio cellist, Edgar Lustgarten, to come over and read through them. He added Chuck Domanico on bass and Emil Richards on percussion because he wanted the group to sound like wood, and because all but one of them could improvise in odd meters. Herb Alpert green-lit the project at A&M and Stephan Goldman produced it. The Roger Kellaway Cello Quartet (A&M, 1971) has "Sunrise" in 15/8 and "Esque" in 5/4, and Joe Pass on two tracks. The name was a filing accident: the music for the group sat in a stack labelled "Cello Quartet," the way another stack was labelled "Sax Quartet," and the label stuck even though there was only ever one cellist. The Center of the Circle (1972) and Come to the Meadow (1974) followed on A&M, and the title tune of the latter became the theme for NPR's Selected Shorts. In 1978 the band expanded to a quintet with the drummer Joe Porcaro for the direct-to-disc Nostalgia Suite. The three A&M records got Kellaway called the father of crossover, a description he has said he will happily take.

The television credit that made him famous outside jazz arrived the same way, by referral. Dave Grusin, busy with a film for Norman Lear's partner Bud Yorkin, passed the job along. Kellaway read the pilot script for All in the Family and wrote a theme without knowing that Lee Adams and Charles Strouse had already been hired to write "Those Were the Days," then played his piece in Hollywood for the director John Rich, Norman Lear and Carroll O'Connor. They took it at once. For the first six episodes both themes ran over the closing credits until his wife Jorjana suggested telling Lear that one would do, which made "Remembering You" the show's closer and, by Kellaway's account, made All in the Family the first American series with different opening and closing themes. O'Connor received a lyric credit, though the words were never used at the end. The theme carried over into Archie Bunker's Place. Around twenty film scores followed, among them Paper Lion (1968), The Mouse and His Child (1977), The Mafu Cage (1978), The Silent Scream (1980), Evilspeak (1981) and Breathless (1983), and his adaptation score for the 1976 A Star Is Born, with Barbra Streisand, brought an Academy Award nomination. Concert commissions ran alongside: PAMTGG, a ballet for George Balanchine and New York City Ballet that premiered at the New York State Theater on June 17, 1971 and was built out of a Pan Am television jingle by Stan Applebaum and Sid Woloshin, plus orchestral pieces for the New York Philharmonic, the Los Angeles Philharmonic and the Cincinnati Symphony, and chamber works for Yo-Yo Ma, the Juilliard String Quartet, James Galway and the tuba player Roger Bobo.

From the mid-1980s he turned back to jazz nearly full-time, and the partnership that defined the next stretch was with the bassist Red Mitchell, who had settled in Stockholm. Kellaway counts eight years and eight records together, several of them taped in Mitchell's own apartment: Alone Together (Dragon, 1988), Some O' This and Some O' That with the clarinetist Putte Wickman (Dragon, 1990) and That Was That with the trumpeter Jan Allan (Dragon, 1991). Concord issued his solo Live at Maybeck Recital Hall, Volume Eleven in 1991 and, the following year, Life's a Take, a duo with Mitchell recorded in the same room. In 1988 he won the Grammy for Best Instrumental Arrangement for Eddie Daniels's Memos from Paradise, an album subtitled "The Music of Roger Kellaway." He served as musical director for a Carnegie Hall tribute to Oscar Peterson and for Stéphane Grappelli's eightieth-birthday concert, at which Yo-Yo Ma made his jazz debut; the studio album that came out of that association, "Anything Goes" (CBS, 1989), credits Kellaway with the arrangements, the music direction and the piano.

His late catalog belongs largely to IPO Recordings, much of it made at his own Kellaway LightWorks studio in Ojai, California: I Was There, drawn from the Bobby Darin songbook (2004), Remembering Bobby Darin (2005), Heroes (2006), a tribute to the Oscar Peterson trio that won the French Jazz Academy's Prix du Jazz Classique, and Live at the Jazz Standard (2008), a quintet with Russell Malone, Jay Leonhart, Stefon Harris and the cellist Borislav Strulev. A long duo relationship with Eddie Daniels produced A Duet of One (2008), Live at the Library of Congress, recorded in the Coolidge Auditorium on February 25, 2011, and Duke at the Roadhouse: Live in Santa Fe, which took the same academy's Grand Prix. He led the band for Van Morrison's Astral Weeks concerts at the Hollywood Bowl on November 7 and 8, 2008. He marked his eightieth birthday in November 2019 with two nights at New York's Birdland Theater backed by the guitarist Roni Ben-Hur and the bassist Jay Leonhart. In 2023 the SmallsLIVE Foundation gave him its Living Masters award, which came with two nights at Mezzrow and a recording; Live at Mezzrow (Cellar Music, 2024), taped on May 5, 2023 with Leonhart, the drummer Dennis Mackrel and Ben-Hur as special guest, is his most recent album.

Kellaway is one of the very few players whose technique is large enough to make the question of category irrelevant, which is exactly why his career reads as scattered until you listen to it. The line runs from Fats Waller and stride through George Shearing, Billy Taylor, Oscar Peterson and Horace Silver, and then straight into Stravinsky, Schoenberg, Messiaen, Berio, Varese and John Cage, all of which he was absorbing simultaneously as a teenager and a Conservatory student who spent alternate Sundays improvising twelve-tone accompaniments to poetry readings. Accompanying is the skill the older players hired him for. Asked how he approached Ben Webster, his answer was to listen to every note and stay out of the way of the sound, and the same discipline is audible behind Wes Montgomery, Sonny Rollins and Carmen McRae. As a writer he works from an ensemble idea rather than a chord sheet, which is what produced the Cello Quartet, a group with no precedent and no imitators that put him at the head of what the industry later called crossover, and it is why a Balanchine ballet, an All in the Family theme and a solo recital at Maybeck Recital Hall can sit in the same catalog without any of them sounding like a detour. The Penguin-era consensus on his solo playing holds up: he is a maximalist who never loses the tune, and reviewers of the Maybeck record and the Red Mitchell duos keep returning to the same two things, an orchestral left hand and a wit that comes out in the way he reharmonizes a standard mid-chorus.