Objection 1. It would seem that the form of this sacrament is not: "I absolve thee." Because the forms of the sacraments are received from Christ's institution and the Church's custom. But we do not read that Christ instituted this form. Nor is it in common use; in fact in certain absolutions which are given publicly in church (e.g. at Prime and Compline and on Maundy Thursday), absolution is given not in the indicative form by saying: "I absolve thee," but In the deprecatory form, by saying: "May Almighty God have mercy on you," or: "May Almighty God grant you absolution and forgiveness." Therefore the form of this sacrament is not: "I absolve thee."
Objection 2. Further, Pope Leo says (Ep. cviii) that God's forgiveness cannot be obtained without the priestly supplications: and he is speaking there of God's forgiveness granted to the penitent. Therefore the form of this sacrament should be deprecatory.
Objection 3. Further, to absolve from sin is the same as to remit sin. But God alone remits sin, for He alone cleanses man inwardly from sin, as Augustine says (Contra Donatist. v, 21). Therefore it seems that God alone absolves from sin. Therefore the priest should say not: "I absolve thee," as neither does he say: "I remit thy sins."
Objection 4. Further, just as our Lord gave His disciples the power to absolve from sins, so also did He give them the power "to heal infirmities," "to cast out devils," and "to cure diseases" (Matthew 10:1; Luke 9:1). Now the apostles, in healing the sick, did not use the words: "I heal thee," but: "The Lord Jesus Christ heal [Vulgate: 'heals'] thee," as Peter said to the palsied man (Acts 9:34). Therefore since priests have the power which Christ gave His apostles, it seems that they should not use the form: "I absolve thee," but: "May Christ absolve thee."
Objection 5. Further, some explain this form by stating that when they say: "I absolve thee," they mean "I declare you to be absolved." But neither can this be done by a priest unless it be revealed to him by God, wherefore, as we read in Matthew 16:19 before it was said to Peter: "Whatsoever thou shalt bind upon earth," etc., it was said to him (Matthew 16:17): "Blessed art thou Simon Bar-Jona: because flesh and blood have not revealed it to thee, but My Father Who is in heaven." Therefore it seems presumptuous for a priest, who has received no revelation on the matter, to say: "I absolve thee," even if this be explained to mean: "I declare thee absolved."
On the contrary, As our Lord said to His disciples (Matthew 28:19): "Going... teach ye all nations, baptizing them," etc., so did He say to Peter (Matthew 16:19): "Whatsoever thou shalt loose on earth," etc. Now the priest, relying on the authority of those words of Christ, says: "I baptize thee." Therefore on the same authority he should say in this sacrament: "I absolve thee."
I answer that, The perfection of a thing is ascribed to its form. Now it has been stated above (1, ad 2) that this sacrament is perfected by that which is done by the priest. Wherefore the part taken by the penitent, whether it consist of words or deeds, must needs be the matter of this sacrament, while the part taken by the priest, takes the place of the form.
Now since the sacraments of the New Law accomplish what they signify, as stated above (62, 1, ad 1), it behooves the sacramental form to signify the sacramental effect in a manner that is in keeping with the matter. Hence the form of Baptism is: "I baptize thee," and the form of Confirmation is: "I sign thee with the sign of the cross, and I confirm thee with the chrism of salvation," because these sacraments are perfected in the use of their matter: while in the sacrament of the Eucharist, which consists in the very consecration of the matter, the reality of the consecration is expressed in the words: "This is My Body."
Now this sacrament, namely the sacrament of Penance, consists not in the consecration of a matter, nor in the use of a hallowed matter, but rather in the removal of a certain matter, viz. sin, in so far as sins are said to be the matter of Penance, as explained above (Article 2). This removal is expressed by the priest saying: "I absolve thee": because sins are fetters, according to Proverbs 5:22. "His own iniquities catch the wicked, and he is fast bound with the ropes of his own sins." Wherefore it is evident that this is the most fitting form of this sacrament: "I absolve thee."
Reply to Objection 1. This form is taken from Christ's very words which He addressed to Peter (Matthew 16:19): "Whatsoever thou shalt loose on earth," etc., and such is the form employed by the Church in sacramental absolution. But such absolutions as are given in public are not sacramental, but are prayers for the remission of venial sins. Wherefore in giving sacramental absolution it would not suffice to say: "May Almighty God have mercy on thee," or: "May God grant thee absolution and forgiveness," because by such words the priest does not signify the giving of absolution, but prays that it may be given. Nevertheless the above prayer is said before the sacramental absolution is given, lest the sacramental effect be hindered on the part of the penitent, whose acts are as matter in this sacrament, but not in Baptism or Confirmation.
Reply to Objection 2. The words of Leo are to be understood of the prayer that precedes the absolution, and do not exclude the fact that the priest pronounces absolution.
Reply to Objection 3. God alone absolves from sin and forgives sins authoritatively; yet priests do both ministerially, because the words of the priest in this sacrament work as instruments of the Divine power, as in the other sacraments: because it is the Divine power that works inwardly in all the sacramental signs, be they things or words, as shown above (62, 4; 64, 1,2). Wherefore our Lord expressed both: for He said to Peter (Matthew 16:19): "Whatsoever thou shalt loose on earth," etc., and to His disciples (John 20:23): "Whose sins you shall forgive, they are forgiven them." Yet the priest says: "I absolve thee," rather than: "I forgive thee thy sins," because it is more in keeping with the words of our Lord, by expressing the power of the keys whereby priests absolve. Nevertheless, since the priest absolves ministerially, something is suitably added in reference to the supreme authority of God, by the priest saying: "I absolve thee in the name of the Father, and of the Son, and of the Holy Ghost," or by the power of Christ's Passion, or by the authority of God. However, as this is not defined by the words of Christ, as it is for Baptism, this addition is left to the discretion of the priest.
Reply to Objection 4. Power was given to the apostles, not that they themselves might heal the sick, but that the sick might be healed at the prayer of the apostles: whereas power was given to them to work instrumentally or ministerially in the sacraments; wherefore they could express their own agency in the sacramental forms rather than in the healing of infirmities. Nevertheless in the latter case they did not always use the deprecatory form, but sometimes employed the indicative or imperative: thus we read (Acts 3:6) that Peter said to the lame man: "What I have, I give thee: In the name of Jesus Christ of Nazareth, arise and walk."
Reply to Objection 5. It is true in a sense that the words, "I absolve thee" mean "I declare thee absolved," but this explanation is incomplete. Because the sacraments of the New Law not only signify, but effect what they signify. Wherefore, just as the priest in baptizing anyone, declares by deed and word that the person is washed inwardly, and this not only significatively but also effectively, so also when he says: "I absolve thee," he declares the man to be absolved not only significatively but also effectively. And yet he does not speak as of something uncertain, because just as the other sacraments of the New Law have, of themselves, a sure effect through the power of Christ's Passion, which effect, nevertheless, may be impeded on the part of the recipient, so is it with this sacrament. Hence Augustine says (De Adult. Conjug. ii): "There is nothing disgraceful or onerous in the reconciliation of husband and wife, when adultery committed has been washed away, since there is no doubt that remission of sins is granted through the keys of the kingdom of heaven." Consequently there is no need for a special revelation to be made to the priest, but the general revelation of faith suffices, through which sins are forgiven. Hence the revelation of faith is said to have been made to Peter.
It would be a more complete explanation to say that the words, "I absolve thee" mean: "I grant thee the sacrament of absolution."
Source: Summa Theologica (New Advent)