Born in Zoppola, Celso Costantini studied in Rome, where he obtained his doctorates in philosophy and theology. He was ordained to the priesthood on December 26, 1899, and then did pastoral work until 1914 in Concordia, where he was also elected as capitular vicar. During World War I, Costantini was a military chaplain in the Italian Army. He served as Concordia's vicar general from 1919 to 1920, when he was made Apostolic Administrator of Fiume on May 10. He died in Rome, at age 82. He is buried next to his brother Giovanni, who also entered religion, in his native Zoppola.