Objection 1. It would seem that it is not proper to Christ to be the Redeemer, because it is written (Psalm 30:6): "Thou hast redeemed me, O Lord, the God of Truth." But to be the Lord God of Truth belongs to the entire Trinity. Therefore it is not proper to Christ.
Objection 2. Further, he is said to redeem who pays the price of redemption. But God the Father gave His Son in redemption for our sins, as is written (Psalm 110:9): "The Lord hath sent redemption to His people," upon which the gloss adds, "that is, Christ, who gives redemption to captives." Therefore not only Christ, but the Father also, redeemed us.
Objection 3. Further, not only Christ's Passion, but also that of other saints conduced to our salvation, according to Colossians 1:24: "I now rejoice in my sufferings for you, and fill up those things that are wanting of the sufferings of Christ, in my flesh for His body, which is the Church." Therefore the title of Redeemer belongs not only to Christ, but also to the other saints.
On the contrary, It is written (Galatians 3:13): "Christ redeemed us from the curse of the Law, being made a curse for us." But only Christ was made a curse for us. Therefore only Christ ought to be called our Redeemer.
I answer that, For someone to redeem, two things are required--namely, the act of paying and the price paid. For if in redeeming something a man pays a price which is not his own, but another's, he is not said to be the chief redeemer, but rather the other is, whose price it is. Now Christ's blood or His bodily life, which "is in the blood," is the price of our redemption (Leviticus 17:11-14), and that life He paid. Hence both of these belong immediately to Christ as man; but to the Trinity as to the first and remote cause, to whom Christ's life belonged as to its first author, and from whom Christ received the inspiration of suffering for us. Consequently it is proper to Christ as man to be the Redeemer immediately; although the redemption may be ascribed to the whole Trinity as its first cause.
Reply to Objection 1. A gloss explains the text thus: "Thou, O Lord God of Truth, hast redeemed me in Christ, crying out, 'Lord, into Thy hands I commend my spirit.'" And so redemption belongs immediately to the Man-Christ, but principally to God.
Reply to Objection 2. The Man-Christ paid the price of our redemption immediately, but at the command of the Father as the original author.
Reply to Objection 3. The sufferings of the saints are beneficial to the Church, as by way, not of redemption, but of example and exhortation, according to 2 Corinthians 1:6: "Whether we be in tribulation, it is for your exhortation and salvation."
Source: Summa Theologica (New Advent)