The orchestra was founded in 1970 by Leonard Slatkin when he was assistant conductor of the SLSO. The assistant conductor (now called Resident Conductor) of the SLSO acts as the music director of the SLSYO. Past SLSYO music directors have included Gerhardt Zimmermann, , , and Scott Parkman. Several of the SLSYO's past members have joined the SLSO in future years, including Mark Sparks (flute), Felicia Foland (bassoon), Rebecca Boyer Hall and Kristin Ahlstrom (violin) and Sarah Hogan (double bass).
Since the start of the 2008-2009 concert season, the American conductor Ward Stare is the conductor of the SLSYO, as part of his duties as Resident Conductor of the SLSO.