A native of Corsicana, Texas, Newman attended Jarvis Christian College where he studied theology on a music scholarship while working with local bands. This led to Newman leaving after two years and hitting the road full-time with Red Connor's group which featured Ornette Coleman and with the band of Charlie Parker's mentor Buster Smith, playing dance halls throughout the southwest. While on tour he met Ray Charles, who was working as a sideman with another group. The two bonded, both musically and personally, and when Charles began leading his own band in 1954, he called upon Newman to join the group, beginning a twelve-year association with the organization, helping to define the Charles orchestra's sound as its star tenor soloist.

Charles was instrumental in helping Newman set out on a solo career, bringing the saxophonist to his label, Atlantic Records, leading to his debut album as a leader in 1959, Fathead: Ray Charles Presents David Newman. The date included Newman's soulful rendition of Paul Mitchell's classic "Hard Times," with which he would be identified for the rest of his life. Newman would record numerous records as a leader for Atlantic. His versatility on saxes and flutes also made him a first call session player and his presence contributed to studio dates by the likes Aretha Franklin, B.B. King, Dr. John, Joe Cocker, The Average White Band, and Garland Jeffreys, as well as Jazz greats Lee Morgan, Herbie Mann, and fellow Charles alumnus Hank Crawford.

Starting in 1980, Newman recorded several Jazz albums on Muse Records, Atlantic records, Herbie Mann's Kokopelli label, and then High Note records. He continued to produce music until last year with his final album being 2008's Diamondhead.

Newman appeared on many television shows, appeared in Robert Altman's film Kansas City, and did a national tour with the Kansas City Orchestra for Verve Records. He was portrayed by Bookeem Woodbine in the feature film Ray, the award-winning movie on the life of Ray Charles starring Jamie Foxx.