As the Holy See has not posted its own translation of the full Italian text, below is our humble translation.
Dear Brothers and Sisters!
The Latin liturgy celebrates today the feast of the Chair of St. Peter. It comes from a very ancient tradition, chronicled at Rome from the end of the 4th century, which renders thanks to God for the mission entrusted to the Apostle Peter and to his successors. The "cathedra," literally, is the fixed seat of the Bishop, found in the mother church in a diocese, which for this reason is called "cathedral," and is the symbol of the authority of the Bishop and, in particular, of his "magisterium," the evangelical teaching which he, as a successor of the Apostles, is called to maintain and pass on to the Christian community. When the Bishop takes possession of the particular Church entrusted to him, he, wearing the mitre and carrying the pastoral staff, is seated in the cathedra. From that seat he will guide, as teacher and pastor, the path of the faithful in faith, in hope and in love.
What was, then, the "cathedra" of St. Peter? He, chosen by Christ as the "rock" on which the Church was built, began his ministry in Jerusalem, after the Ascension of the Lord and Pentecost. The first "see" of the Church was the Cenacle, and it's likely that in that room, where also Mary, the mother of Jesus, prayed together with the disciples, a special place was reserved for Simon Peter. Successively, the see of Peter became Antioch, a city situated on the Oronte River, in Syria, today in Turkey, in that time the third metropolis of the Roman empire after Rome and Alexandria in Egypt. From that city, evangalized by Barnabas and Paul, where "for the first time the disciples were called Christians" (Acts 11:26), where the name Christian was born for us, Peter was the first bishop, so that the Roman Martyrology, before the reform of the calendar, also provided for a specific celebration of the Chair of Peter at Antioch. From there, Providence brought Peter to Rome. Therefore we have the road from Jerusalem, the newborn Church, to Antioch, the first center of the Church recounted by the Pagans and still united with the Church which proceeded from the Jews. Then Peter came to Rome, center of the Empire, symbol of the "Orbis" -- the "Urbs" [city] which expresses the "Orbis" [world] of the earth -- where he concluded with his martyrdom his course in the service of the Gospel. For this, the see of Rome, which received the greatest honor, is also accorded the honors entrusted by Christ to Peter to be at the service of all the particular Churches for the building up and the unity of the entire People of God.
The see of Rome, after this movement of St. Peter, became recognized as that of the successor of Peter, and the "cathedra" of its bishop represented that of the Apostle charged by Christ to feed his flock. This is attested to by the most ancient Fathers of the Church, for example St. Iraneus, bishop of Lyon, but living in Asia Minor, who in his treatise Against heresies described the Church of Rome as "the greatest and most ancient, known of all;... founded and built at Rome by the two most glorious apostles Peter and Paul"; and then: "With this Church, for its outstanding superiority, must be accorded to it the Church universal, the faithful in every place" (III, 3, 2-3). Tertullian, a little later, for his part, affirms: "How blessed is this Church of Rome! For it the apostles poured out, with their blood, the whole of doctrine." The chair of the Bishop of Rome represents, therefore, not only its service to the Roman community, but its mission of watching over the entire People of God.
To celebrate the "Cathedra" of Peter, as we do today, means, then, to attribute to it a strong spiritual significance and to recognize it as a privileged sign of the love of God, the good and eternal Shepherd, who wishes to gather the entire Church and guide it along the way of salvation. Among the many testimonies of the Fathers, I'd like to report that of St. Jerome, who wrote in a letter of his to the Bishop of Rome, particularly interesting because it makes an explicit reference to the "chair" of Peter, presented it as the sure grounding of truth and of peace. As Jerome wrote: "I decided to consult the chair of Peter, where is found that faith which the mouth of an Apostle exalted; I come then to ask nourishment for my soul, where once was received the garment of Christ. I don't follow a primate other than Christ; for this reason, I place myself in communion with your blessedness, that is, with the chair of Peter. I know that on this rock is built the Church" (Letters I, 15, 1-2).
Dear Brothers and Sisters, in the apse of St. Peter's Basilica, as you know, can be found the monument to the Chair of the Apostle, Bernini's eldest work, realized in the form of a great bronze throne, held up by statues of four Doctors of the Church, two of the west, St. Augustine and St. Ambrose, two of the east, St. John Chrysostom and St. Athanasius. I invite you to stand in front of this suggested work, which today is probably decorated admirably by many candles, and pray in a particular way for the ministry which God has entrusted to me. Raising our gaze to the alabaster window which opens over the Chair, invoking the Holy Spirit, may he always sustain with his light and strength my daily service to all the Church. [Applause] For this, and for your devoted attention, I thank you from my heart.