Joseph Silverstein began his musical studies with his father, Bernard. He continued with Josef Gingold, and, at the Curtis Institute, where he graduated in 1950, studied with Efrem Zimbalist and Veda Reynolds. He then held positions with the orchestras of Houston, Philadelphia, and Denver before joining the Boston Symphony Orchestra in 1955 as its youngest player.

In 1959 he won third prize (silver medal) in the Queen Elisabeth Competition, and in 1960 he won the Naumburg Award. In 1962 he was appointed concertmaster of the Boston Symphony Orchestra, and he became its assistant conductor in 1971. He served as music director of the Utah Symphony for fifteen years and was named its conductor laureate in 1998.

A member of the Chamber Music Society of Lincoln Center, Joseph Silverstein performs frequently in New York and has appeared as a soloist and conductor with more than one hundred orchestras in the United States, Japan, Israel, and throughout Europe.

He has served on the faculties of Yale and Boston Universities, New England Conservatory, and Tanglewood Music Center, and he has recorded for such labels as RCA, Deutsche Grammophon, Delos, CBS, Nonesuch, EMI, and Image. He joined the faculty of the Curtis Institute of Music in 2000.