He was ordained to the priesthood on 17 May 1856, by Costantino Patrizi Naro, Cardinal Vicar General of Rome.

He returned to the diocese of Mantua, where he worked as a professor of ecclesiastical history, moral theology, and canon law at its seminary.

He became Bishop of Pavia in 1871, being consecrated on 5 November of that year in the church of Santissima Trinità al Monte Pincio by Cardinal Patrizi Naro.

Parocchi was created Cardinal-Priest of San Sisto Vecchio by Pope Pius in the consistory of 22 June 1877.

Pope Leo appointed him as Secretary of the Supreme Sacred Congregation of the Holy Office on 5 August 1896, a post he held until his death.