Walter Norris was born December 27, 1931, in Little Rock, Arkansas, the son of Lucian Norris, an accountant at the Federal Reserve Bank. He started classical piano at five with his mother and continued with John Summers, a local church organist, and by twelve he was playing in Little Rock bands. His first steady professional work came with the Howard Williams Band around Little Rock while he was still at Central High School. After graduating he toured briefly with Mose Allison, then served in the U.S. Air Force from 1950 to 1952. Discharged, he worked with trumpeter Jimmy Ford in Houston before taking a residency at the El Morocco in Las Vegas, dated by the Encyclopedia of Arkansas to 1953 and 1954, and then moving to Los Angeles.

The Los Angeles years put him inside the West Coast scene at its peak. He held down two years of house work at the Haig and the Tiffany Club, sharing bandstands with Frank Rosolino, Stan Getz and Dexter Gordon, and toured with Nat King Cole. His recording debut came in 1954 on trumpeter Jack Sheldon's first album, the 10-inch Get Out of Town (Jazz: West JWLP-1), with Ralph Peña on bass and Gene Gammage on drums; Rosolino's Frankly Speaking for Capitol followed in 1955, and alto saxophonist Herb Geller's Stax of Sax (Jubilee 1094) in 1958. That same year Norris took the piano chair on the session that still defines him to most listeners. Over three dates at Contemporary's Los Angeles studio, February 10, February 22 and March 24, 1958, he recorded Something Else!!!! The Music of Ornette Coleman (Contemporary C 3551) with Coleman on alto, Don Cherry on cornet, Don Payne on bass and Billy Higgins on drums, Lester Koenig producing and Roy DuNann engineering. It was Coleman's first record, and the last one on which he used a pianist: from Tomorrow Is the Question! onward Coleman dropped the instrument entirely, which left Norris in the odd position of being permanently filed under free jazz on the strength of a single conventionally voiced bebop-quintet date.

Norris moved to New York in 1960 and formed a trio with guitarist Billy Bean and bassist Hal Gaylor, an unusual piano-guitar-bass group with no drummer. Orrin Keepnews recorded it for Riverside on June 6 and 30, 1961 as The Trio (RLP 380); a second set of the group's tapes, dated by the liner notes to roughly 1958 and 1959, surfaced only in 2000 as Rediscovered on the British String Jazz label. In 1963 Norris took a job at the New York Playboy Club, first as house pianist and eventually as the club's director of entertainment, staying until 1970 while studying piano and conducting at the Manhattan School of Music. The Playboy years kept him solvent and largely off record, and he spent 1970 to 1974 freelancing and teaching around New York.

In 1974 he replaced Roland Hanna in the Thad Jones/Mel Lewis Orchestra, the Village Vanguard Monday-night band, and stayed roughly two years, touring Europe, Japan and the United States with it. The orchestra's New Life (Dedicated to Max Gordon) (A&M/Horizon SP-707, 1976), cut at A&R Recording in New York on December 17, 1975 and January 8 and 10, 1976, splits the piano chair between Norris and Hanna and was nominated for a Grammy in the big-band category. Europe took hold of him quickly. After a Scandinavian tour he stayed on in Munich long enough to record his first album for Enja, the duo Drifting with bassist George Mraz, taped at the Trixi studio on August 18, 1974. A year later, on August 13, 1975, he was at the Domicile in Munich for the live date that produced two Enja LPs under Pepper Adams's name, Julian and Twelfth & Pingree, with Mraz and the South African drummer Makaya Ntshoko. The same stretch put him on drummer Klaus Weiss's The Git Go for MPS and on Frank Foster's Japanese big-band album Giant Steps, a Columbia/Denon date staffed largely out of the Thad Jones/Mel Lewis book.

The move to Germany was made under duress. Back in the United States, Norris joined Charles Mingus's quintet in 1976 and, by his own account, made the mistake of addressing the bassist as "Charlie" in the dressing room before a set. The stage manager's call to the bandstand cut off the confrontation, and Norris left the band. He accepted an offer to play in the orchestra of Sender Freies Berlin, the West Berlin public broadcaster, and moved to the city in January 1977, saying afterward that fear of Mingus was the real reason he emigrated. He had in fact already recorded with the SFB Big Band, on Paul Kuhn's Pop à la Swing for EMI in 1975. Berlin became permanent. The broadcasting work supported a run of duo records for Enja with the Hungarian bassist Aladár Pege, Synchronicity, taped live at the East-West Jazz Festival in Nuremberg on May 5, 1978, and Winter Rose, recorded digitally on three days in 1980 at Tonstudio Bauer in Ludwigsburg. On a New York visit he cut a trio session for Gus Statiras at Downtown Sound on July 17, 1978 with Mraz and drummer Ronnie Bedford; it appeared first in Japan as A Child Is Born (Progressive/Teichiku KUX-161-G, 1981) and then in the United States as Stepping on Cracks (Progressive PRO 7039, 1982). From the early 1980s he taught piano improvisation at the Hochschule der Künste in Berlin, later holding a professorship there, and he described the arrangement as the reason he could live an ordinary middle-class life as a jazz musician.

American attention returned in 1990, when Concord signed him to a five-album contract. Live at Maybeck Recital Hall, Volume Four (CCD-4425), a solo recital taped in Berkeley in April 1990 with liner notes by Leonard Feather, was followed by the trio album Lush Life (CCD-4457, September 1990) with Neil Swainson and Harold Jones, the quartet Sunburst (CCD-4486, August 13 and 14, 1991) with Joe Henderson, Larry Grenadier and Mike Hyman, Love Every Moment (CCD-4534, 1992) with Putter Smith and Larance Marable, and a second Mraz duo, Hues of Blues (CCD-4671, May 1995). In between he had taken the piano chair for Chet Baker's final concert, played with the NDR Bigband and the Radio Orchestra Hannover under Dieter Glawischnig at the Funkhaus in Hannover on April 28, 1988; Baker was dead in Amsterdam two weeks later, and the recording was issued by Enja as My Favourite Songs: The Last Great Concert. After the Concord contract lapsed Norris financed his own records: From Another Star, a duo with bassist Mike Richmond cut in Brooklyn in October 1998 and pressed in an edition of 1,000, and Elements in Motion, taped with Putter Smith at his Berlin home in July 2006. He published an autobiography, In Search of Musical Perfection, and a method book, Essentials for Pianist Improvisers, in 2005, and Chuck Dodson completed a documentary about him in 2010. Arkansas claimed him twice, with induction into the state's Jazz Hall of Fame in 1995, the same year Steinway named him a Steinway Artist, and into the Arkansas Entertainers Hall of Fame in 2003. His last recorded performance was a two-piano set with the Polish pianist Leszek Możdżer at the A-Trane in Berlin on November 2, 2008, released posthumously by ACT as The Last Set. Norris passed away at his Berlin home on October 29, 2011, at seventy-nine, survived by his wife Kirsten.

Norris built his playing on a formidable classical technique used for jazz ends: fast, evenly weighted lines with a hard rhythmic displacement running under them, so that the beat stayed unambiguous while the phrasing kept landing somewhere other than expected. He wrote most of his own material, and pieces like "Space Maker," "Rose Petals" and "Scrambled" set deliberate technical traps that he then played through at tempo. Joe Morgenstern, writing the notes for Sunburst, described him approaching each tune the way a lapidary studies a stone before cutting it, then going through with startling accuracy, and the two Concord duo and trio dates with George Mraz show why: the harmony is dense and constantly re-voiced, but nothing is smudged. His own standard repertoire ran to John Coltrane's "Naima" and "Giant Steps," Charlie Parker's "Bird" and Thad Jones's "A Child Is Born," which he recorded three separate times. The persistent misfiling of Norris as an avant-gardist, on the strength of Something Else!!!! and thirty-four years of living abroad, irritated the critics who did follow him; American writers of the 1990s tended to open their reviews by pointing out that he was neither obscure nor a free player, just a bebop-rooted pianist with an unusually complete command of the instrument who happened to live in Berlin. As a teacher at the Hochschule der Künste he refused textbooks and lectures, saying he wrote prescriptions instead: a student played, and he told them what was right or wrong with it.