Eli Eban was appointed principal clarinetist of the Jerusalem Symphony Orchestra under Lukas Foss immediately after graduating from the Curtis Institute of Music. Shortly thereafter he joined the Israel Philharmonic Orchestra at the invitation of Zubin Mehta. During thirteen seasons with the Israel Philharmonic, he performed and recorded all the major orchestral repertoire with the world's leading conductors, including Claudio Abbado, Leonard Bernstein, Christoph von Dohnanyi, Charles Dutoit, Christoph Eschenbach, James Levine, Kurt Masur, Simon Rattle, Georg Solti, Kryzstof Penderecki, and Lorin Maazel.

Eban was the featured soloist with the Israel Philharmonic Orchestra on many occasions, and he has also performed concertos with the English Chamber Orchestra, the Salzburg Camerata Academica , the City of London Sinfonia, the Chamber Orchestra of Philadelphia, Louisville Orchestra, and the Israel Camerata/Jerusalem, among others. He tours extensively as a chamber musician, collaborating with renowned artists and ensembles. He has been guest artist with the Alexander, Audubon, Orion, St. Petersburg, Tel Aviv and Ying quartets and was a frequent participant of the famed Marlboro Music Festival. While at Marlboro, Eban was selected by legendary violinist Sandor Vegh to be the first wind player to perform at the prestigious IMS Prussia Cove festival in England, drawing acclaim from the London "Guardian" for his "high-powered, electrifying performances". His subsequent recordings for Meridian Records, London, were cited by critics as being "full of life and highly sensitive". He has also recorded for the Saphir, Crystal and Naxos labels. He was a member of "Myriad" (a chamber ensemble formed by members of the Cleveland Orchestra) and has often traveled to Eastern Europe to perform and teach at the invitation of the European Mozart Foundation.

Eli Eban was a visiting professor at the Eastman School of Music for two years before joining the faculty of the Jacobs School of Music at Indiana University, where he holds a distinguished ranks' Rudy professorship. His former students are pursuing active solo careers and have won orchestral positions in Israel, Denmark, Korea, Poland, Singapore, and South Africa. In the USA they can be heard in the symphony orchestras of Indianapolis, New Mexico, Toledo, the New World Symphony and in the premier service bands in Washington, D.C. He divides his time between teaching at the Jacobs School of Music, touring as a soloist and chamber musician, and serving as the principal clarinetist of the Indianapolis Chamber Orchestra. His summers are spent performing and teaching at the Sarasota Music Festival and playing principal clarinet in the Chautauqua Symphony Orchestra.