Alex Norris grew up in Columbia, Md. where he began studying music at the age of 9. After graduating high school he received a scholarship to the Peabody Conservatory of Music to study trumpet. He graduated from the Conservatory in 1990.
In 1992, Norris moved to New York City to pursue a career as a jazz trumpeter.. Here, he found work with the Village Vanguard Jazz Orchestra, Toshiko Akiyoshi's Jazz Orchestra, and Maria Schneider's Band. From 1994-1998, Norris was a member of Betty Carter's Jazz Ahead, becoming musical director in 1998; the final year of Carter's life. Norris has also performed and recorded extensively in the bands of Lonnie Plaxico, Jason Lindner, and with Ralph Irizarry's Timbalaye.
Norris has worked with many noted jazz musicians such as Slide Hampton, Joshua Redman, Brad Mehldau, Chris Potter, Carl Allen, John Patitucci, Mulgrew Miller, and Brian Blade. Norris is very active in Afro-Cuban jazz, as well, having worked with Andy and Jerry González, Manny Oquendo, Paquito D’Rivera, and Chico O’Farril.
In 1995, Norris received a master's degree from the Manhattan School of Music. He has served on the music faculties at the New School of Jazz and Contemporary Music, Towson University, and the City College of New York. In 2007, Norris received a Doctor of Musical Arts degree from the University of Miami Frost School of Music. From 2005-2008, Norris was also a teacher at the University of Miami.