From the Catholic Encyclopedia:
It is the teaching of the Council of Trent that the form of the Sacrament of Penance, wherein its force principally consists, is placed in these words of the minister, “I absolve thee”; to which words certain prayers are, according to the custom of Holy Church, laudably added etc. (Sess. XIV, iii). That the public penance was concluded with some sort of prayer for pardon, is the doctrine of antiquity, particularly as contained in the earliest sacramentaries (Duchesne, Christian Worship, 440, 441). Leo the Great (450) does not hesitate to assert that pardon is impossible without the prayer of the priest (“ut indulgentia nisi supplicationibus sacerdotum nequeat obtineri”). In the early Church these forms certainly varied (Duchesne, loc. cit.). Surely all the sacramentaries assert that the form was deprecatory, and it is only in the eleventh century that we find a tendency to pass to indicative and personal formulæ (Duchesne, loc. cit.). Some of the forms used at the transition period are interesting: “May God absolve thee from all thy sins, and through the penance imposed mayst thou be absolved by the Father, the Son, the Holy Ghost, by the Angels, by the Saints, and by me, a wretched sinner” (Garofali, Ordo ad dandam pœnitentiam, 15). Then come really indicative and personal formulæ, often preceded by the supplicatory prayer, “Misereatur tui” etc. These forms, while much the same in substance, vary in wording not a little (Vacant, Dict. de théol. 167). It was not until the scholastic doctrine of “matter and form” in the sacraments reached its full development that the formula of absolution became fixed as we have it at present. The form in use in the Roman Church today has not changed since long before the Council of Florence. It is divided into four parts as follows: —
(1) Deprecatory prayer. "May the Almighty God have mercy on you, and forgiving your sins, bring you to life everlasting. Amen." Then, lifting his right hand towards the penitent, the priest continues: "May the Almighty and Merciful God grant you pardon, absolution, and remission of your sins".
(2) "May Our Lord Jesus Christ absolve you, and I, by His authority, absolve you from every bond of excommunication [suspension, in the case of a cleric only] and interdict as far as I can and you may need."
(3) "I absolve you from your sins in the name of the Father, and of the Son, and of the Holy Ghost. Amen." (While repeating the names of the Trinity, the priest makes the sign of the cross over the penitent.)
(4) "May the Passion of Our Lord Jesus Christ, the merits of the Blessed Virgin Mary and of all the Saints, what good you have done or what evil you have suffered be to you for the remission of (your) sins, growth in grace and the reward of everlasting life. Amen." In the decree "Pro Armenis", 1439,** Eugene IV teaches that the "form" of the Sacrament is really in those words of the priest: "Ego absolvo te a peccatis tuis in nomine Patris" etc., and theologians teach that absolution would be valid should the priest use, "Absolvo te", "Absolvo te a peccatis tuis", or words that are the exact equivalent ** (Suarez, Disp., XIX, i, n. 24; Lugo, Disp., XIII, i, nn. 17, 18; Lehmkuhl, de Pœnit., 9th ed., 199).