2 For Christ was not anointed by men with oil or material ointment, but the Father having before appointed Him to be the Saviour of the whole world, anointed Him with the Holy Ghost, as Peter says, Jesus of Nazareth, whom God anointed with the Holy Ghost. David also the Prophet cried, saying, Your throne, O God, is for ever and ever; a sceptre of righteousness is the sceptre of Your kingdom; You have loved righteousness and hated iniquity; therefore God even Your God has anointed You with the oil of gladness above Your fellows. And as Christ was in reality crucified, and buried, and raised, and you are in Baptism accounted worthy of being crucified, buried, and raised together with Him in a likeness, so is it with the unction also. As He was anointed with an ideal oil of gladness, that is, with the Holy Ghost, called oil of gladness, because He is the author of spiritual gladness, so you were anointed with ointment, having been made partakers and fellows of Christ.
Source: Catechetical Lectures (New Advent)