The hypostatic union refers as you probably know to the union of the two natures, namely the divine and the human, in the one divine person of Jesus Christ. The fathers of the fourth ecumenical council of the Church, the Council of Chalcedon (451), dogmatically defined that Jesus Christ is one divine person in two complete and unmixed natures. The divine person of Jesus Christ is the second person of the Trinity, namely, the Son of God. The Son of God is the Word, as St John says in the beginning of his gospel, who became flesh and dwelt among us. The Son of God became incarnated in the most pure womb of the Virgin Mary.
Jesus Christ is true God and true man. Jesus Christ is true God because the person of Jesus Christ is none other than the Son of God, the second person of the Trinity. At the fiat of the Virgin Mary, the eternal Son of God united to his divine nature, a human nature, namely, that of a true man. This occurred without the Son of God losing nothing of his divinity. The two natures in Jesus Christ are united in such a way in the person of the Son of God that the two natures are whole and complete in themselves; they are not mixed together so as to form some kind of mixture or nature of divine and human nature.