Giacomo was the son of Domenico Sartori, a barber, and Hedwig Lutteri. He started in his father's profession, and it was initially thought that he would continue in his father’s business. However he became a self-taught mandolinist, wrote his first composition at age 18, and in March 1881 enrolled as an "apprentice violin" to the Musical Society of Ala.
He furthered his musical studies in Rovereto, as a student of Tito Brogialdi for violin and Giovanni Toss for composition. In Ala, where he continued to live, he soon became an important musical figure, as teacher, a conductor of the local band, and organist in the parish.
His first known public performance was on 26 January 1888 in the Philharmonic Hall of Ala, where he played the violin fantasy from ‘Roberto the Devil’ by G. Meyerbeer, with Lorenzo Frelich on the piano.
In 1889 he married Elvira Wagmeister from Appiano, by whom he had four sons. During the First World War he became a refugee in Verona, where he often played first violin in symphony concerts.
After the war, in 1919, he did not return to Ala, but moved to Trento, and devoted himself entirely to music. Here, until 1938, he directed the mandolin orchestral ensemble " Club Armonia" in place of Vigil Kirchner, performing in many places in South Tyrol and in various cities of Italy.
As a connoisseur of plectrum instruments he began to write for mandolins and guitars (solo, quartet and orchestral works), and a series of his compositions were printed on a regular basis, especially in the Turin newspaper "Il Mandolino" from 1894-1939, and on the pages of "Mandolinista Italiano”in Milan.
His works were well reviewed abroad, and he received no less than seven prestigious, international prizes. His music was widely used throughout Europe until the Second World War, and reflects his respect for the Italian tradition of melodic and popular musical themes, elegies, serenades, and dances.
He died in Trento in 1946. The city of Ala honoured him by naming the city theatre the “Giacomo Sartori Theatre”. An international mandolin competition, Concorso Giacomo Sartori, held in Ala, is dedicated to his name.