Queyras was born in Montreal on March 11, 1967. Part of his childhood was spent in Algeria, which was unusual since this period postdated Algeria's independence from France after a bloody independence war. Queyras' family ultimately moved to France, where Queyras took cello lessons. He studied at various institutions, including the Musikhochschule Freiburg in Germany and the Mannes College of Music in New York before coming under the influence of Boulez and joining his famous contemporary music ensemble. Queyras' recording career began in 1994, thanks to his presence in the Boulez orbit, when he was heard on a Deutsche Grammophon recording featuring various concertos by György Ligeti, conducted by Boulez. His next recording came in 1998 on the Harmonia Mundi label; it featured the Three Suites for Solo Violoncello of Benjamin Britten. Queyras has often performed music for solo cello, including the unaccompanied cello suites of J.S. Bach.
Queyras' discography is large and includes releases on the BIS and Erato labels as well as Harmonia Mundi (which is home to the majority). He has recorded mainstream works by Brahms, Elgar, and Dvořák as well as contemporary and Baroque works. In 2020, Queyras and pianist Alexandre Tharaud released Complices, a program of brief transcriptions conceptualized as short stories. Queyras teaches at the Musikhochschule Freiburg and is an artistic director at the Rencontres Musicales de Haute Provence music festival.