Monti was born in Como. He studied for the Catholic priesthood at the Villoresi di Monza seminary. He was ordained as a priest in 1879. The Bishop of Como encouraged Monti to study theology in Rome. Monti received his degree in theology in 1880. His first job as a priest was in Urio, a small town in Province of Como. Then he was a priest at the church of San Giorgio in Como until 1881. After 1881 he was the chaplain of the church's cemetery.
He was very active in the cultural life of Como. In 1888 he became vice-president of the Como Historical Society. In 1906 he became the president of the society. He served as the president until he died in 1923. He was also the curator of the Civic Museum of Como and a member of the Provincial Commission for the Conservation of Monuments. Monti died in Como.
- "Necrologio. Canonico Cav. Don Santo Monti", in Periodico della Società Storica della Provincia e antica Diocesi di Como (1924), Vol. XXV, p. 3