At times people think the ten commandments themselves are the covenant. They are at the heart of it, but there is a bit more to it.
Exo 34:27 And the LORD said to Moses, "Write these words, for in accordance with these words I have made a covenant with you and with Israel."
Exo 34:28 So he was there with the LORD forty days and forty nights. He neither ate bread nor drank water. And he wrote on the tablets the words of the covenant, the Ten Commandments.
Exo 34:29 When Moses came down from Mount Sinai, with the two tablets of the testimony in his hand as he came down from the mountain, Moses did not know that the skin of his face shone because he had been talking with God.
It is very clear that the ten commandments on stone played an important role in the covenant. They are called the words of the covenant. They are like a covenant document.
Deu 4:13 And he declared to you his covenant, which he commanded you to perform, that is, the Ten Commandments, and he wrote them on two tablets of stone.
A covenant is an agreement with promises on both sides between multiple parties. And the ten commandments are the covenant words, or document, but not the totality of the agreement.The initial covenant agreement happened at Sinai, and was re-affirmed at various times.
The description of the covenant agreement is found in
Exodus 19 and 20.
Exo 19:3 while Moses went up to God. The LORD called to him out of the mountain, saying, "Thus you shall say to the house of Jacob, and tell the people of Israel:
Exo 19:4 You yourselves have seen what I did to the Egyptians, and how I bore you on eagles' wings and brought you to myself.
Exo 19:5 Now therefore, if you will indeed obey my voice and keep my covenant, you shall be my treasured possession among all peoples, for all the earth is mine;
Exo 19:6 and you shall be to me a kingdom of priests and a holy nation. These are the words that you shall speak to the people of Israel."
God sets forth promises for the people if they will obey the terms of His covenant.
Moses then relays this to the people who respond:
Exo 19:7 So Moses came and called the elders of the people and set before them all these words that the LORD had commanded him.
Exo 19:8 All the people answered together and said, "All that the LORD has spoken we will do." And Moses reported the words of the people to the LORD.
So we have promises on both sides. God will bless them and they will be His people. They agree to do all that the Lord commands.
This is the covenant. But it is spelled out in detail from there out.
The covenant agreement included a number of items. At the center of the covenant were the ten commandments which became the covenant contract document.
We know from near-eastern covenants of the time that God was doing something that would be familiar. The type of covenant in question is known as a suzerainty covenant. It was usually made between two nations, when a stronger kingdom conquered another. The Suzerain was the powerful king and benefactor (sometimes conquerer) the other king was his vassal.
The stronger king would impose the treaty upon the vassal king in order to make plain his requirements and how they were to serve him. He would make promises to them in return for their loyalty. Now of course in this case the great King is God and the vassal nation are His people. He delivered them from another nation and on this basis, and on the basis of creation, He demonstrates that He is their Sovereign. So He puts this in familiar terms, and we see a number of parallels to covenants of that time.
Here is a file that illustrates the key components of a suzerainty treaty in brief form. This is not my work. I just found it to be the simplest I could find online.
http://www.bethel.edu/~dhoward/classes/Ot101-111/SuzeraintyTreaty-Handout.pdf
Now if we look at the various components it outlines how the Sinai covenant is similar.
1. Preamble: Identifies author of the covenant.
Exo 20:2 "I am the LORD your God,
2. Historical Prologue: Mentions past relationship between the two parties; past benefactions by suzerain form the basis for the vassal's gratitude and future obedience.
Exo 19:3 while Moses went up to God. The LORD called to him out of the mountain, saying, "Thus you shall say to the house of Jacob, and tell the people of Israel:
Exo 19:4 You yourselves have seen what I did to the Egyptians, and how I bore you on eagles' wings and brought you to myself.
Ex. 20:2 Who brought you out of the land of Egypt, out of the house of slavery.
3. Stipulations: The obligations laid upon the vassal by the sovereign.
The ten commandments, and then also the book of the law, including all the laws of the nation, laws regarding worship, laws of a moral nature, laws instituting care for the poor, etc.
All of these were required of Israel under the covenant, and part of their agreement to do all the Lord commanded.
4. a. Deposition: A copy of the covenant is deposited in the vassal's sanctuary.
In the normal arrangement each party would place a copy of the covenant in the sanctuary of their god's temple. In this case one party IS God and the others worship at His temple. Therefore the covenant document is placed in stone, and placed in the temple of God, inside the ark. Many scholars now think the whole text was written on each, as a copy for God and a copy for the people, but this is not an essential element here and is not spelled out in the biblical text, so I don't think we can be dogmatic on the point. But it may explain the emphasis on the two tablets.
b. Public Reading: The covenant terms are periodically read to the people.
This occurred during the invasion into Canaan, and later during the time of the restoration from exile, etc.
5. Witnesses: A list of gods invoked to witness the covenant.
God, being the only true God, calls upon the creation in Deut.:
Deu 30:19 I call heaven and earth to witness against you today, that I have set before you life and death, blessing and curse. Therefore choose life, that you and your offspring may live,
6. Curses invoked on the vassal if he breaks the covenant, and blessings invoked on the vassal if he keeps the covenant.
Leviticus 26 etc. spells these out in detail. A brief version of the benefits of being God's people occurs in Ex. 19:
A google search on suzerainty covenant will bring up a number of other resources for further study on the subject.