Born in 1924 in Zurich, Varviso studied several instruments at that city's conservatory and went on to Austria to study conducting with the legendary Clemens Krauss of the Vienna State Opera and Philharmonic. He began working at the Basel Opera and got his first music director appointment there in 1956; he remained in the post up to 1962. From 1965 to 1971 he served as music director of Sweden's Royal Opera in Stockholm (receiving the title of "Court Conductor" in 1970); he later held the same position at the W‹rttemberg State Opera in Stuttgart (1972-1980) and the Op_ra de Paris (1980-1985).

Varviso conducted at many other major houses in Europe, including the Vienna State Opera, the Deutsche Oper Berlin, the Bavarian State Opera in Munich, the Royal Opera House (Covent Garden) in London and the Glyndebourne, Salzburg and Bayreuth Festivals. He made his U.S. debut at the San Francisco Opera in 1959 and led the American premiere of Britten's A Midsummer Night's Dream there in 1960; his Metropolitan Opera debut, in 1961, was conducting a Lucia di Lammermoor starring Joan Sutherland and Richard Tucker.

Among Varviso's several recordings are a Barbiere di Siviglia with Teresa Berganza, Donizetti's Anna Bolena with Marilyn Horne, Bellini's La sonnambula with Sutherland, Verdi's Don Carlo with Plšcido Domingo and Mascagni's Cavalleria rusticana with Mario del Monaco.

Known for his versatility, Varviso had a repertoire ranging from Mozart and Strauss to Puccini to Prokofiev, from Wagner to Bellini to Debussy. As recently as last season — at age 81 — he learned a new opera: Donizetti's Maria Stuarda, which he conducted in Antwerp and Ghent.