He studied music at the Conservatoire de Paris and the Schola Cantorum with Leroux, Georges Caussade, d'Indy and others.
He remained in Montparnasse, Paris until 1922 and he maintained close relations with artistic circles that included Casella, Ravel, Varèse and Modigliani, whose last painting was a portrait of Varvoglis.
After 1920 he taught at the Athens Conservatory and he became active as a music critic and conductor.
He was persecuted for his liberal political views and he was imprisoned in a British concentration camp during the Dekemvriana He died in Athens.
Varvoglis' music belongs to the Greek national school, but was also influenced by the French style.