Varviso studied at the Zurich Conservatory conducting, piano, violin, clarinet, trumpet and percussion. When Clemens Krauss in Vienna, he completed his studies. In St. Gallen, he was with Wolfgang Amadeus Mozart's Magic Flute his debut to 1962 to change as musical and artistic director at the Stadttheater Basel. From 1965 to 1971, Varviso music director at the Royal Opera in Stockholm, then in the same capacity from 1972 to 1979 at the Stuttgart Opera. This led him to collaborate with major directors, such as Jean- Pierre Ponnelle in Wagner's Ring of the Nibelung or with Götz Friedrich in Claude Debussy's Pelléas et Mélisande, Wolfgang Amadeus Mozart's Così fan tutte, Richard Strauss' Salome, Wagner's Parsifal and Puccini's La Bohème. As a conductor, he was appointed to senior positions in major opera houses in Europe and the United States. Between 1960 and 1980, Silvio Varviso was one of the most famous guest conductors and led almost every famous orchestras in western Europe, especially in the performance of operas and festivals. In the 1960s and 1970s, he took countless concerts on record. Varviso performed with the Vienna Philharmonic Orchestra on several occasions at the Salzburg Festival. He also led the Chicago Symphony Orchestra, the Royal Philharmonic Orchestra and the San Francisco Symphony Orchestra.
For many years Varviso was as a guest conductor at the Vienna State Opera, worked at the Royal Opera House, at the Deutsche Oper Berlin, the Hamburg State Opera, the Bavarian State Opera, the Frankfurt Opera and the Paris Opera. In 1961 was the conductor of its U.S. debut, first at the San Francisco Opera, and later at the Metropolitan Opera in New York, where he conducted Gaetano Donizetti's Lucia di Lammermoor with the also debuting Joan Sutherland. From 1969 to 1974 he conducted at the Bayreuth Festival, The Flying Dutchman, Lohengrin and Die Meistersinger von Nürnberg. In 1983 he returned to the Metropolitan and there conducted Wagner's Die Walküre and the following season Gioachino Rossini's Il Barbiere di Siviglia. From 1991, he was a regular guest conductor at the Vlaamse Opera in Antwerp and Ghent, where he oversaw a highly regarded Puccini cycle, directed by Robert Carsen musical. Shortly before his death he conducted in September 2006 in Antwerp Puccini's Tosca. The conductor had lived since the death of his wife retired in Basel.
Varviso received numerous honors and awards. King Gustav VI. Adolf of Sweden awarded him the title of a Court Kapellmeister in Stuttgart him an honorary doctorate was awarded by Prime Minister Lothar Späth.