Ted Nash was born December 28, 1960, in Los Angeles, into a family already working in Hollywood's studio and big-band scene: his father, Dick Nash, was a trombonist and first-call studio musician, and his uncle, also named Ted Nash (1922 to 2011), was a saxophonist and clarinetist who spent decades in the bands of Les Brown and elsewhere. Both men worked regularly with Henry Mancini, and the younger Nash grew up around that circle rather than discovering jazz from a distance. He started piano at seven, took up clarinet at twelve, and moved to alto saxophone at thirteen. At sixteen he played a week with Lionel Hampton, and the following year he was already sitting in with Quincy Jones, Louie Bellson, and Don Ellis, an association that produced his earliest documented recording credit, Raincheck, billed to "The Louie Bellson Quintet Featuring Ted Nash" (1978). At eighteen he moved to New York and joined the Gerry Mulligan Big Band, and that same year he recorded his debut album as a leader, Conception (Concord Jazz), released in 1979 with bassist Bob Magnusson and drummer Jeff Hamilton.

Through the 1980s Nash held a saxophone chair in the Mel Lewis Jazz Orchestra at the Village Vanguard, where he also began writing arrangements for the band, a role documented on the live album Soft Lights and Hot Music (1988) alongside fellow reed players Dick Oatts, Joe Lovano, Ralph Lalama, and Gary Smulyan. He studied privately with vibraphonist Charlie Shoemake during these years as well. After Mel Lewis's death in 1990, Nash stayed with the band through its transition into the Vanguard Jazz Orchestra, appearing on the posthumous tribute To You: A Tribute to Mel Lewis (1991).

In the 1990s Nash built a parallel career as a composer and small-group leader. He recorded as a sideman with Wynton Marsalis, Joe Lovano, and bassist Ben Allison, and at Allison's invitation joined the Herbie Nichols Project, a repertory band devoted to the compositions of pianist Herbie Nichols that recorded Love Is Proximity (1996), Dr. Cyclops' Dream (1999), and Strange City (2001). He was also a founding member of the Jazz Composers Collective, the New York non-profit that produced those records. His own leader dates from the period include European Quartet (1994, Elabeth), Rhyme & Reason (1999, Arabesque), billed to the Ted Nash Double Quartet and pairing a jazz rhythm section with a string quartet, and Sidewalk Meeting (2001, Arabesque), on which trombonist Wycliffe Gordon guests. He continued the Palmetto Records run with Still Evolved (2003), La Espada de la Noche (2005), and In the Loop (2006), all recorded with a working quartet of Ben Allison, pianist Frank Kimbrough, and drummer Matt Wilson, then closed out the label relationship with The Mancini Project (2008), a tribute to Henry Mancini that connected back to his own father's and uncle's studio work with the composer.

Nash joined the reed section of the Jazz at Lincoln Center Orchestra under Wynton Marsalis in the 1990s and held the chair until 2024, becoming one of the orchestra's principal composers as well as one of its saxophonists. His seven-movement suite Portrait in Seven Shades (2010, Jazz at Lincoln Center, Inc.), dedicated to Claude Monet, Salvador Dali, Henri Matisse, Pablo Picasso, Vincent van Gogh, Marc Chagall, and Jackson Pollock, was recorded live at Frederick P. Rose Hall on September 6, 2007, with bandmates Walter Blanding, Sherman Irby, Victor Goines, and Ali Jackson, and drew a Grammy nomination.

His next commission for the orchestra became his best-known work. Presidential Suite: Eight Variations on Freedom (2016, Motema), recorded September 14, 2014, interweaves eight original compositions with recorded and live readings of historic political speeches by Winston Churchill, Franklin D. Roosevelt, John F. Kennedy, Lyndon B. Johnson, Nelson Mandela, Jawaharlal Nehru, Aung San Suu Kyi, and Ronald Reagan, read by Sam Waterston, actress Glenn Close, Senator Joe Lieberman, and Marsalis himself among others. At the 59th Grammy Awards in February 2017, the album won Best Large Jazz Ensemble Album, and its movement "Spoken at Midnight" won Nash a second Grammy that night, for Best Instrumental Composition.

Separately from the Jazz at Lincoln Center Orchestra, Nash leads his own Ted Nash Big Band, a sixteen-piece ensemble whose 2013 album Chakra (Plastic Sax Records), a seven-movement suite, carries clarinetist and tenor saxophonist Anat Cohen in the reed section alongside bassist Martin Wind. Nash also plays alto and soprano saxophone and flute on Cohen's own large-ensemble leader date, Noir (2007, Anzic Records), billed to Anat Cohen & The Anzic Orchestra. Since 2018 he has been a third of an ongoing working trio with bassist Ben Allison and guitarist Steve Cardenas, releasing a new songbook-tribute album roughly every two years, among them Somewhere Else: West Side Story Songs (2019) and Healing Power: The Music of Carla Bley (2022), before the trio's first album of original material, Triological (2026). His more recent leader projects have moved outside the working-band format entirely: Transformation (2021, Tiger Turn), a full-length vocal collaboration with Close, and Holidays (2023, Sunnyside), a big-band Christmas record made with vocalist Kristen Lee Sergeant. He also appears as featured soprano and alto saxophone soloist, rather than as composer or leader, on Migrations (2019, Naxos), a suite composed by clarinetist Derek Bermel for the Juilliard Jazz Orchestra and the Albany Symphony Orchestra with vocalist Luciana Souza.

Nash's defining trait is range rather than a single voice: across a discography built on alto, soprano, and tenor saxophones, clarinet, bass clarinet, flute, and piccolo, he moves between hard-swinging big-band writing, chamber-jazz settings for strings, and large-scale programmatic suites without treating any of them as a departure from the others. That instinct for structure, rather than pure improvisation, defines his composing: Portrait in Seven Shades sets a movement to each of seven painters' visual styles, and Presidential Suite interlocks original music with the cadences of real political speech, a format its own liner notes and reviewers compared to Oliver Nelson's 1967 Kennedy tribute The Kennedy Dream. His two Grammy wins for Presidential Suite, one for the album and one for a single movement's composition, reflect that same double identity as both a bandstand saxophonist and a large-ensemble composer, a combination the Jazz at Lincoln Center Orchestra relied on across three decades of commissions.