At the Passover, when Jesus said, "Take, eat, this is my body... take, drink, this is the New Testament in my blood, which is given and shed for you for the forgiveness of sins," he wasn't inventing a "new" thing.
Likewise, when the apostle Paul writes to the Corinthian church, "The cup of blessing which we bless, is it not a participation in the blood of Christ? The bread which we break, is it not a participation in the body of Christ?", he's not imagining some new way of worship. He's drawing a direct line from Israel's history to the present tense. The roots of the Lord's Supper, as it's often called, reach far down into Israel's history.
One of the earliest examples of this happens in Genesis 4:10. Cain, the elder brother, murders his little brother, the good shepherd, Abel. Then, the Lord says to Cain, "Your brother's blood cries out to me from the dirt. Hebrews 12:24 teaches that Abel's blood cried out for grace, not judgment. In a similar but more powerful way, Jesus' blood cries out even more graciously. Already in Genesis, we learn that the blood of the good shepherd cries out for grace.
Jumping ahead in Genesis [14:18] the king, Melchizedek., brought Abraham bread and wine after his victory at Chedorlaomer. King Melchizedek was also a "priest of the Most High God." Why does this king-priest, who has no beginning or end in the story, bring Abraham bread and wine? To celebrate Abraham's victory over the enemy.
Also of importance, Melchizedek's name means "King of Righteosuness," and he comes from Salem, which means "Peace." Melchizedek is king of righteousness and king of peace. That is, the king of righteousness brings bread and wine from the city of peace to celebrate a victory. When you read Genesis, it doesn't get more Christ-focused than that!
When Moses, the first Israelite priest, stood before the six hundred thousand person congregation at Mount Sinai, he read the Torah to them. After he'd read the Word of God he threw the blood of sacrificed oxen on them, and said: "Behold the blood of the covenant promise which the Lord has made with you" (Exodus 24:8). Later, at the Last Supper, Jesus concludes the old covenant promise when he said, "This is the New Testament in my blood, given and shed for you..." (Matthew 26:28).
Finally, when Moses came down from Mount Sinai with the tablets of the testimony the skin on his face shined because he'd been talking with the Lord. When he walked into the Israelite camp they asked that he cover his face, because the glory was too much for them to bear. Moses covered his face then with a veil. This same veil covers God's glory every time the Lord's Supper is celebrated. Jesus, God's Word in the flesh, the glory of God, comes veiled under simple earthly bread and wine, which he says is his flesh and is his blood.
How can this be? We don't know. The apostle calls it a "mystery." That is, now we see in faith, then at the Last Day we'll see in fact. All we know now is that the same Word that said, "Let there be light, and there was light," is the same Word that says, "This is my body... this is my blood." When God speaks he acts, and when he acts he speaks. They're one and the same thing for God's Word.