Final answer:
Moses transferred the priestly powers to his brother Aaron, establishing the hereditary Aaronic priesthood according to the Book of Exodus in the Bible.
Step-by-step explanation:
The individual whom Moses transferred the priestly powers to was his brother, Aaron. According to the Book of Exodus in the Bible, Moses, at the command of God, anointed Aaron and his sons to serve as priests. This event is significant as it establishes the hereditary Aaronic priesthood in the Israelite tradition, which is a pivotal moment in Jewish history and religion. The anointing of Aaron and his sons is a highly symbolic act, marking them as God's chosen priests to perform the sacred rituals and sacrifices on behalf of the people of Israel.