See the subsection “the Church in Prophecy” in this article for a summary:
Also, from Pope Benedict XVI:
March 15, 2006 General Audience
An evident sign of the intention of the Nazarene to gather together the community of the Covenant, to demonstrate in it the fulfilment of the promises made to the Fathers who always speak of convocation, unification, unity, is the institution of the Twelve. We heard about this institution of the Twelve in the Gospel reading. I shall read the central passage again: “And he went up into the hills and called to him those whom he desired; and they came to him. And he appointed twelve to be with him, and to be sent out to preach and have authority to cast out demons. The names of the twelve Apostles are these…” (Mk 3: 13-16; cf. Mt 10: 1-4; Lk 6: 12-16).
The number 12, which evidently refers to the 12 tribes of Israel, already reveals the meaning of the prophetic-symbolic action implicit in the new initiative to re-establish the holy people. As the system of the 12 tribes had long since faded out, the hope of Israel awaited their restoration as a sign of the eschatological time (as referred to at the end of the Book of Ezekiel: 37: 15-19; 39: 23-29; 40-48).
In choosing the Twelve, introducing them into a communion of life with himself and involving them in his mission of proclaiming the Kingdom in words and works (cf. Mk 6: 7-13; Mt 10: 5-8; Lk 9: 1-6; 6: 13), Jesus wants to say that the definitive time has arrived in which to constitute the new People of God, the people of the 12 tribes, which now becomes a universal people, his Church.
Equating the two has been common since the beginning:
St. Justin Martyr, Dialogue with Trypho:
For the true spiritual Israel, and descendants of Judah, Jacob, Isaac, and Abraham (who in uncircumcision was approved of and blessed by God on account of his faith, and called the father of many nations), are we who have been led to God through this crucified Christ, as shall be demonstrated while we proceed.
Pope Gregory XVI, Quo Graviora:
We, therefore, who have been constituted as the Guardian of the House of Israel, which is Holy Church, and who in accord with Our Pastoral Office ought to beware lest the Lord’s flock divinely entrusted to Us suffer any harm…
Benedict XIV, Ubi Primum:
When the Prince of Shepherds appears, you will receive an unfading crown of glory and a crown of justice which is reserved for those faithful dispensers of the mysteries of God and for those energetic and vigilant observers of the house of Israel, the Holy Church of God.
Second Vatican Council:
Israel according to the flesh, which wandered as an exile in the desert, was already called the Church of God.(96) So likewise the new Israel which while living in this present age goes in search of a future and abiding city (97) is called the Church of Christ.(98)
Thus the Apostles were the first budding-forth of the New Israel…