Philip Wells Woods was born November 2, 1931, in Springfield, Massachusetts. At twelve he inherited a saxophone left behind by an uncle, and his first teacher, Harvey LaRose, pointed him toward improvisation and the records of Benny Carter and Duke Ellington. By sixteen Woods was traveling to New York to study privately with Lennie Tristano, and in 1948 he enrolled at Juilliard, majoring in clarinet while working jazz gigs at night; he briefly played in Charlie Barnet's dance band during his student years and graduated in 1952. His fast, harmonically dense alto style, indebted to Charlie Parker without copying him outright, soon earned him the nickname "the New Bird," a tag also given at various points to contemporaries Sonny Stitt and Cannonball Adderley.

Through the mid-1950s Woods worked with bandleaders George Wallington, Kenny Dorham, and Buddy Rich, and in 1956 he joined Dizzy Gillespie's big band, beginning a friendship in which Gillespie acted as mentor in both music and life for years afterward. That same year, at twenty-four, Woods took part in a State Department-sponsored tour of the Middle East and South Asia organized by Quincy Jones, and appeared on the Birdland All-Stars package tour. His recording debut as a leader, Woodlore (Prestige, 1956), paired him with bassist Teddy Kotick and drummer Nick Stabulas. The following year he co-led The Young Bloods (Prestige) with trumpeter Donald Byrd, a quintet date with pianist Al Haig, Kotick again on bass, and drummer Charlie Persip. Around this period Woods married Chan Parker, Charlie Parker's widow, and became stepfather to her daughter, singer Kim Parker; the marriage lasted seventeen years, ending in divorce in 1973. Woods's twin-alto partnership with Gene Quill later in the 1950s, documented on a run of sextet and studio dates, helped cement his reputation as one of the most in-demand altoists in New York, and in 1958 he recorded eight tracks of Michel Legrand's Legrand Jazz (Columbia), four of them alongside Miles Davis, John Coltrane, and Bill Evans in the same personnel.

The 1960s brought Woods's fullest statement as a composer and bandleader to that point, Rights of Swing (Candid, 1961), a four-part suite for a nine-piece band including Curtis Fuller, Julius Watkins, Benny Bailey, and Sahib Shihab. Alongside his own dates, he became a fixture of Quincy Jones's touring and recording orchestra through the early 1960s and of Oliver Nelson's sessions, including More Blues and the Abstract Truth (Impulse!, 1964), and he traveled to the Soviet Union in 1962 as part of Benny Goodman's state-sponsored tour. In 1968 Woods relocated to France and, after working through a shifting cast of European musicians including pianist George Gruntz, formed the European Rhythm Machine with pianist Gordon Beck, bassist Henri Texier, and drummer Daniel Humair, a trio whose freer, more exploratory book was documented on live recordings from the Frankfurt Jazz Festival (1970, released on Embryo) and the Montreux Jazz Festival. A separate 1969 studio session, Round Trip (Verve), paired Woods with an American cast, Thad Jones, Herbie Hancock, Roland Hanna, Richard Davis, and Grady Tate, apart from the touring trio.

Woods returned to the United States in 1972 and settled in the Delaware Water Gap area of Monroe County, Pennsylvania, where he lived for the rest of his life. In 1973 he formed the working band that became his defining vehicle: pianist Mike Melillo, bassist Steve Gilmore, and drummer Bill Goodwin, briefly expanded with guitarist Harry Leahey. That lineup's Live From The Showboat (RCA Victor, 1977), recorded at a Silver Spring, Maryland club in November 1976, launched the group nationally and won the Grammy Award for Best Jazz Performance by a Group at the 20th Annual Grammy Awards. Gilmore and Goodwin anchored the band for more than forty years, one of the longest unbroken rhythm-section partnerships in jazz, while the piano chair passed from Melillo (1974-1981) to Hal Galper (1981-1990), Jim McNeely (1990-1995), and Bill Charlap (1996-2008), and a horn partner was added in October 1982: trumpeter Tom Harrell stayed until 1989, succeeded by trombonist Hal Crook and then, from January 1992, trumpeter Brian Lynch. The quartet's 'More' Live (Adelphi, 1981) and At the Vanguard (Antilles, 1983) each won Grammy Awards for Best Instrumental Jazz Performance, Group, at the 25th and 26th Annual Grammy Awards, following an earlier win for Images (RCA Victor, 1975), arranged and conducted by Michel Legrand, at the 18th Annual Grammy Awards.

Woods's studio work crossed well outside jazz in the mid-1970s: his alto solo on Steely Dan's "Doctor Wu" (Katy Lied, 1975) and on Paul Simon's "Have a Good Time" (Still Crazy After All These Years, 1975) preceded his best-known recording to a general audience, the solo on Billy Joel's "Just the Way You Are" (The Stranger, 1977), which introduced his playing to millions of listeners who had never heard a jazz record. He continued composing throughout his life, more than 200 pieces in all, and in 1978 co-founded the Celebration of the Arts (COTA) festival near his Pennsylvania home. He was inducted into the American Jazz Hall of Fame in 1994 and named a National Endowment for the Arts Jazz Master in 2007, alongside Toshiko Akiyoshi, Curtis Fuller, Ramsey Lewis, Jimmy Scott, and Frank Wess, and received the Kennedy Center's Living Jazz Legend award the same year. He kept recording into his eighties, including The Gershwin Affair (Philology, 2006) with pianist Franco D'Andrea, American Songbook (Kind of Blue, 2006) with Brian Lynch and Bill Charlap, and Man With the Hat (Pazz Productions, 2011), a collaboration with the younger alto saxophonist Grace Kelly.

Woods lived with worsening emphysema through his final years, performing much of his last decade on supplemental oxygen. He gave what is generally cited as his last public performance on September 4, 2015, a tribute to Charlie Parker with strings at the Manchester Craftsmen's Guild in Pittsburgh, announcing his retirement from the stage at its close. He passed away twenty-five days later, on September 29, 2015, in East Stroudsburg, Pennsylvania, at eighty-three.

Woods built his style on Charlie Parker's vocabulary filtered through the harder tone and greater harmonic reach he absorbed from Benny Carter and Johnny Hodges, arriving at a sound fast, precise, and unmistakably his own rather than a copy of Bird's; critics and fellow players nonetheless reached for "the New Bird" for decades. He was equally serious as a writer, from the four-movement suite of Rights of Swing through the freer, more open-ended music of the European Rhythm Machine, and as a bandleader he built, in the quartet and quintet he ran from 1973 until his death, one of the most stable working units in jazz history, with bassist Steve Gilmore and drummer Bill Goodwin at his side for over forty years. His alto solos on Billy Joel's "Just the Way You Are," Steely Dan's "Doctor Wu," and Paul Simon's "Have a Good Time" carried his phrasing to a mainstream pop audience far larger than jazz reaches on its own. He won nearly thirty Down Beat magazine reader and critics' poll awards on alto saxophone across his career.