Strauss was educated by Paul Tortelier and Maurice Gendron at the Conservatoire de Paris, where he won first prizes in cello and in chamber music, before continuing his studies at Yale University with Aldo Parisot.
He has also taught in the Netherlands and sat on the juries on many international music competitions.
Strauss has collaborated with many important contemporary classical composers, including Maurice Béjart, Luciano Berio, Pierre Boulez, Henri Dutilleux, Philippe Hersant, and Krzysztof Penderecki, and is the dedicatee of a number of their works.
As a chamber musician, Strauss has performed with such artists as: pianists Jean-Claude Pennetier, Georges Pludermacher and Henriette Puig-Roget; violinists Gérard Jarry, Tibor Varga, and Sandor Vegh; violists Gérard Caussé, Serge Collot, and Bruno Pasquier; as well as fellow cellist and former teacher Aldo Parisot.
He is the founder and artistic director of the Giverny Chamber Music Festival.