Or HaChaim on Exodus 28:41/אור החיים על שמות כ״ח:מ״א

1 והלבשת אותם…ומשחת אותם, "and you will dress Aaron and his sons in them and anoint them, etc." The Torah means that the priests are first to put on the garments and that they are to be anointed while still wearing these garments. The act of anointing the priests with the anointing oil helped to make them into priests. When the Torah speaks of ומלאת את ידם, instead of merely of ומלאת אותם, this may mean that the priests would be affected emotionally by this procedure so that they would become recipients of G'd's kindness, known as "His great Hand." Students of the Kabbalah will understand what I refer to.

2וקדשת אותם, "and you will sanctify them." This refers to the performance of the sacrificial service which (Moses) would perform in order to sanctify them. This had to be mentioned here in order for us to know that until Aaron and his sons wore the priestly garments and had been anointed, the sacrificial service performed by Moses did not accomplish the change in their status.