30 On the Cross then the Old Law died, soon to be buried and to be a bearer of death, in order to give way to the New Testament of which Christ had chosen the Apostles as qualified ministers; and although He had been constituted the Head of the whole human family in the womb of the Blessed Virgin, it is by the power of the Cross that our Savior exercises fully the office itself of Head of His Church. "For it was through His triumph on the Cross," according to the teaching of the Angelic and Common Doctor, "that He won power and dominion over the gentiles"; by that same victory He increased the immense treasure of graces, which, as He reigns in glory in heaven, He lavishes continually on His mortal members; it was by His blood shed on the Cross that God's anger was averted and that all the heavenly gifts, especially the spiritual graces of the New and Eternal Testament, could then flow from the fountains of our Savior for the salvation of men, of the faithful above all; it was on the tree of the Cross, finally, that He entered into possession of His Church, that is, of all the members of His Mystical Body; for they would not have been untied to this Mystical Body through the waters of Baptism except by the salutary virtue of the Cross, by which they had been already brought under the complete sway of Christ.
Source: Mystici Corporis Christi (Vatican.va)