Norah's earliest musical influences came from her mother's extensive LP collection and from 'oldies' radio. She began singing in church choirs at age five, commenced piano lessons two years later, and briefly played alto saxophone in junior high. When Norah was 15, she and her mother moved from Grapevine to Dallas' central city, where she enrolled in Booker T. Washington High School for the Performing and Visual Arts.

Norah played her first gig on her 16th birthday, an open-mic night at a local coffeehouse, where she performed a version of I'll Be Seeing You that she'd learned from Etta James' treatment of this Billie Holiday favorite. While in high school, Norah won the Down Beat Student Music Awards for Best Jazz Vocalist and Best Original Composition in 1996, and earned a second SMA for Best Jazz Vocalist in 1997. After graduation, she entered the University of North Texas, renowned for its music programs, where she majored in jazz piano. She also sang with a band called Laszlo, playing what she describes as "dark, jazzy rock." In the summer of 1999, Norah accepted a friend's offer of a summer sublet in Greenwich Village. She came to Manhattan and never returned to North Texas State. For about a year beginning in December 1999, Norah appeared regularly with the funk-fusion band Wax Poetic.

But she soon assembled her own group with Jesse Harris, Lee Alexander, and Dan Rieser. In October 2000, this lineup recorded a selection of demos for Blue Note Records. On the strength of these recordings and a live showcase, Jones was signed to Blue Note in January 2001. Norah sang two songs (Roxy Music's More Than This and Day Is Done by Nick Drake) on guitarist Charlie Hunter's Blue Note album Songs from the Analog Playground, and has frequently performed live with Hunter's group. Norah began recording the songs of Come Away With Me in May 2001, doing preliminary work with producer Craig Street at Bearsville Studio in Woodstock, New York. Come Away With Me, produced by soul veteran Arif Mardin, was released to strong critical acclaim in February 2002. Despite featuring support from respected musicians Bill Frisell and Brian Blade, the album was more notable for its pop, country and soul leanings and only briefly strayed into smooth jazz territory. Perplexingly, the album was lodged at the top of the Billboard contemporary jazz album chart for over one consecutive year, from March 2002 to June 2003. After 46 weeks on the mainstream chart, Come Away With Me climbed to the number 1 position in January 2003.