Jesus fulfilled the prophecies of the OT, in particular Isa 53.
Isa 53
1 Who hath believed our report? and to whom is the arm of the LORD revealed?
2 For he shall grow up before him as a tender plant, and as a root out of a dry ground: he hath no form nor comeliness; and when we shall see him, [there is] no beauty that we should desire him.
3 He is despised and rejected of men; a man of sorrows, and acquainted with grief: and we hid as it were [our] faces from him; he was despised, and we esteemed him not.
4 Surely he hath borne our griefs, and carried our sorrows: yet we did esteem him stricken, smitten of God, and afflicted.
5 But he [was] wounded for our transgressions, [he was] bruised for our iniquities: the chastisement of our peace [was] upon him; and with his stripes we are healed.
6 All we like sheep have gone astray; we have turned every one to his own way; and the LORD hath laid on him the iniquity of us all.
7 He was oppressed, and he was afflicted, yet he opened not his mouth: he is brought as a lamb to the slaughter, and as a sheep before her shearers is dumb, so he openeth not his mouth.
8 He was taken from prison and from judgment: and who shall declare his generation? for he was cut off out of the land of the living: for the transgression of my people was he stricken.
9 And he made his grave with the wicked, and with the rich in his death; because he had done no violence, neither [was any] deceit in his mouth.
10 Yet it pleased the LORD to bruise him; he hath put [him] to grief: when thou shalt make his soul an offering for sin, he shall see [his] seed, he shall prolong [his] days, and the pleasure of the LORD shall prosper in his hand.
11 He shall see of the travail of his soul, [and] shall be satisfied: by his knowledge shall my righteous servant justify many; for he shall bear their iniquities.
12 Therefore will I divide him [a portion] with the great, and he shall divide the spoil with the strong; because he hath poured out his soul unto death: and he was numbered with the transgressors; and he bore the sin of many, and made intercession for the transgressors.
Some NT references to Jesus being the Messiah:
Mat 16:16-17
And Simon Peter answered and said, Thou art the Christ, the Son of the living God. 17 And Jesus answered and said unto him, Blessed art thou, Simon Barjona: for flesh and blood hath not revealed [it] unto thee, but my Father which is in heaven.
Jhn 11:27
She saith unto him, Yea, Lord: I believe that thou art the Christ, the Son of God, which should come into the world.
Mar 14:61-62
But he held his peace, and answered nothing. Again the high priest asked him, and said unto him, Art thou the Christ, the Son of the Blessed? 62 And Jesus said, I am: and ye shall see the Son of man sitting on the right hand of power, and coming in the clouds of heaven.
Heb 5:5
So also Christ glorified not himself to be made an high priest; but he that said unto him, Thou art my Son, to day have I begotten thee.
Luk 4:41
And devils also came out of many, crying out, and saying, Thou art Christ the Son of God. And he rebuking them suffered them not to speak: for they knew that he was Christ.