The parish was erected in 1935, and immediately put under the administration of the Friars Minor Capuchin. The church, which was begun in 1934, was completed structurally in the following year. It was built by the Pontifical Opera on a project by the architects Mario Paniconi
and Giulio Pediconi
. On 2 October 1941 the church was consecrated.
There was a restoration of the sanctuary in 1958, when the floor was raised and a new high altar provided.
In July 1968, the Vicariate of Rome approved the fresco in the apse of the church featuring Saint Felix of Cantalice, its namesake patron saint, made by Fr Ugolino de Belluno, a Franciscan priest.