[1] After graduation he moved to in England and Holland to study, and gave his debut concert in London's Wigmore Hall in 1976.
He has performed extensively with his ensembles Tragicomedia and Teatro Lirico,[2][3] and conducted baroque operas worldwide.
There he established the Seattle Academy of Baroque Opera, the Pacific MusicWorks early music performance series, and is an adjunct professor at Cornish College of the Arts.
He is artistic co-director (with Paul O'Dette) of the Boston Early Music Festival.
On February 8, 2015, Stubbs won a Grammy Award for Best Opera Recording for: Charpentier: La descente d'Orphée aux enfers H 488 & La Couronne de fleurs H.486, Paul O'Dette & Stephen Stubbs, conductors; Aaron Sheehan; Renate Wolter-Seevers, producer (Boston Early Music Festival Chamber Ensemble; Boston Early Music Festival Vocal Ensemble).