Rossi opened a hospice for homeless women not long after his ordination, and he became known for his work with prisoners and ill people, to whom he dedicated his entire ecclesial mission.

It had begun decades before but was suspended due to tensions in Europe that meant work could not be pursued regarding the cause; it was later revitalized and he was beatified in 1860.

[4] His initial education was under the care of the two priests Scipio Gaetano and Giuseppe Repetto who noted his potential and brilliance and held him as their favorite student.

Rossi met two Capuchin friars at the Scorza residence one evening who thought well of him and offered to help him continue his studies.

[2][3] At the suggestion of his cousin, Lorenzo de' Rossi, canon of Santa Maria in Cosmedin, he travelled to Rome in 1711 in order to commence his studies at the Collegium Romanum under the guidance of the Jesuits.

[2][1] His cousin Lorenzo wanted him as coadjutor to ensure Rossi would become his successor; Giovanni Battista accepted in February 1735.

Rossi was not authorized due to his condition and resisted it for a while but was consoled when the Bishop of Civitá Castellana Giovanni Francesco Maria Tenderini told him that it was all part of his vocation.

In 1748 his health became weakened to the point that he moved to Santissima Trinità dei Pellegrini but continued to work at Santa Maria in Cosmedin.

Rossi was beatified after Pope Pius IX attributed two miracles to his intercession on 7 March 1859 and presided over the celebration in Saint Peter's Basilica on 13 May 1860.

On 8 December 1881 the acknowledgement of two more miracles in 1881 enabled Pope Leo XIII to canonize him as a saint of the Roman Catholic Church.