Jesus often quoted and referred to the Old Testament Scriptures, including relating Himself to them as the fulfillment. Below are some verses from the Bible on what Jesus said about the Old Testament and Himself.
You search the Scriptures because you think that in them you have eternal life; it is these that testify about Me [John 5:39]
And He said to them, “O foolish men and slow of heart to believe in all that the prophets have spoken! Was it not necessary for the Christ to suffer these things and to enter into His glory?” Then beginning with Moses and with all the prophets, He explained to them the things concerning Himself in all the Scriptures. [Luke 24:25-27]
Now He said to them, “These are My words which I spoke to you while I was still with you, that all things which are written about Me in the Law of Moses and the Prophets and the Psalms must be fulfilled.” Then He opened their minds to understand the Scriptures, and He said to them, “Thus it is written, that the Christ would suffer and rise again from the dead the third day, and that repentance for forgiveness of sins would be proclaimed in His name to all the nations, beginning from Jerusalem. You are witnesses of these things. [Luke 24:44-48]
For if you believed Moses, you would believe Me, for he wrote about Me. But if you do not believe his writings, how will you believe My words? [John 5:46-47]
Do not think that I came to abolish the Law or the Prophets; I did not come to abolish but to fulfill. For truly I say to you, until heaven and earth pass away, not the smallest letter or stroke shall pass from the Law until all is accomplished. [Matthew 5:17-18]
Adapted from The Christian and the Bible Ten Basic Steps Toward Christian Maturity, Step 5 by Bright, Bill (publisher: NewLife Publications)