One of the most in demand jazz drummers in the world today, Jeff initially majored in classical percussion at Pittsburgh's Duquesne University, where he was primarily a timpanist, followed by enrollment at the Berklee School of Music, where he pursued jazz studies alongside such talented players as Branford Marsalis, Kevin Eubanks, Greg Osby, Aimee Mann, Steve Vai and Marvin "Smitty" Smith.
Jeff joined the Wynton Marsalis Quartet in 1981 and proceeded to win three Grammy Awards with the ensemble. Watts left Wynton Marsalis in 1988. After working with George Benson, Harry Connick. Jr. and McCoy Tyner, he joined the Branford Marsalis Quartet in 1989.
Jeff has worked in the film and television industry as both a musician on the Tonight Show with Jay Leno and as an actor, Rhythm Jones in Spike Lee’s "Mo Better Blues". Jeff joined Kenny Garrett's band after returning to New York in 1995 after three years in LA on the Tonight Show. Watts also continued to record and tour with Branford Marsalis as well as Danilo Perez, Michael Brecker, Betty Carter, Kenny Kirkland, Courtney Pine, Geri Allen, Alice Coltrane, Greg Osby, Steve Coleman, Gonzalo Rubalcaba, and Ravi Coltrane.