His original name was Eugene Bibb. He was the son of Eugene Sharp Bibb and Kathleen Palmer Hart. He took the last name Foster after his stepfather, Frohman Foster, who raised him.
Eugene was a noted flutist, who was for many years principal flutist for the Utah Symphony Orchestra. He studied at the Juilliard School of Music and the Curtis Institute, and performed with every U.S. and Canadian tour of the Bolshoi Ballet, as well as the New York Ballet Theater and the Sadlers Wells Ballet. He was offered the position of principal flutist with the Leningrad Philharmonic Orchestra but turned it down.