The Book of the Law started as a scroll or set of scrolls written by Moses, then passed on to the Israelites when Joshua led them into Canaan. Because the scrolls were also used for recording covenants between God & the Israelites, it was kept in the Ark of the Covenant. As such, it was also known as the Book of the Covenant in Exodus 24:7; 2 Kings 23:2,21 and 34:30.
Moses told Joshua to read the Law every 7 yrs. during the Year of Jubilee in Deuteronomy 31:7-13:
7. Then Moses summoned Joshua and said to him in the presence of all Israel, "Be strong and courageous, for you must go with this people into the land that the LORD swore to their forefathers to give them, and you must divide it among them as their inheritance.
8. The LORD himself goes before you and will be with you; he will never leave you nor forsake you. Do not be afraid; do not be discouraged."
9. So Moses wrote down this law and gave it to the priests, the sons of Levi, who carried the ark of the covenant of the LORD, and to all the elders of Israel.
10. Then Moses commanded them: "At the end of every seven years, in the year for canceling debts, during the Feast of Tabernacles,
11. when all Israel comes to appear before the LORD your God at the place he will choose, you shall read this law before them in their hearing.
12. Assemble the people--men, women and children, and the aliens living in your towns--so they can listen and learn to fear the LORD your God and follow carefully all the words of this law.
13. Their children, who do not know this law, must hear it and learn to fear the LORD your God as long as you live in the land you are crossing the Jordan to possess."
The scrolls were misplaced, then they resurfaced during the reign of Judah's king Josiah when they began referring to it as the Book of Moses.
2 Kings & 2 Chronicles have parallel passages regarding the rediscovery of the Book of Moses.