The Old Testament also tells us that the coming Messiah would proclaim Himself the fulfillment of prophecy.
Old Testament Prophecy
Sacrifice and offering you did not desire, but my ears you have pierced; burnt offerings and sin offerings you did not require. Then I said, "Here I am, I have come- it is written about me in the scroll. I desire to do your will, O my God; your law is within my heart." [Psalm 40:6-8 NIV]
New Testament Fulfillment