In the autumn of 1865, he traveled to the United States, where he was ordained to the priesthood by Bishop John Timon, CM, on 4 January 1866, in Buffalo, New York.

[1] Falconio served as administrator, chancellor, and vicar general of Harbor Grace in Canada between 1871 and 1882, and would have become its bishop had not the opposition of the Irish Benevolent Society to the appointment of an Italian bishop caused Falconio's superior to recall him to the United States.

He received his episcopal consecration on the following 17 July from Cardinal Raffaele Monaco La Valletta, with Archbishops Antonio Grasselli, OFM Conv, and Tancredo Fausti serving as co-consecrators, in the church of S. Antonio da Padova in Via Merulana.

Falconio was created Cardinal-Priest of Santa Maria in Aracoeli by Pope Pius X in the consistory of 27 November 1911,[2] and opted to be promoted to Cardinal Bishop of Velletri on 25 May 1914.

He was one of the cardinal electors who participated in the 1914 papal conclave, which selected Pope Benedict XV, who named Falconio Prefect of the Sacred Congregation for Religious on 26 February 1916.