He was born in Montevideo on April 30, 1889. He was the eldest child of the marriage between Camilo Giucci and Luisa Gallo. He began his violin studies at the age of 8 with Virgilio Scarabelli. In 1897 he gave his first concert, at the Franz Liszt Conservatory of Music.

In 1908, he won a competition that awarded him a scholarship to continue his violin studies in Europe. Before leaving, he gave a farewell concert accompanied by the Argentine pianist Ernesto Drangosch. In 1909 he traveled to Germany to study at the Royal Academy of Music in Berlin, where Carl Flesch and Henri Marteau were his teachers. The following year he returned to Montevideo for a few months and gave some concerts.

In 1913, he returned to live permanently in Montevideo. After the passing of his father in December of that year, he took over the management of the Franz Liszt Conservatory of Music, a role he held until he passed away. In 1915, he abandoned his career as a concert artist and devoted himself entirely to his role as a teacher and director of the Conservatory of Music. In addition to his classes at the Conservatory, in 1953 he held the chair of violin at the National Conservatory.

Camilo Giucci passed away on January 7, 1973.