He received his doctorate in mathematics in 1899 from the University of Palermo with a thesis on celestial mechanics and continued his interest in astronomy by working until 1903 at Palermo Astronomical Observatory (osservatorio astronomico cittadino), which was under the direction of Annibale Riccò.

From 1903 to 1923 Cantelli worked at the Istituto di Previdenza della Cassa Depositi e Prestiti (Pension Fund for the Government Deposits and Loans Bank).

Cantelli made fundamental contributions to the foundations of probability theory and to the clarification of different types of probabilistic convergence.

[1] He was the founder of the Istituto Italiano degli Attuari for the applications of mathematics and probability to economics.

Cantelli was the editor of the Giornale dell'Istituto Italiano degli Attuari (GIIA) from 1930 to 1958.