Gen 3:15, 2 Sam 7:12-17, Acts 13:22-23,34-38
God had long spoken through the mouths of the prophets that He would send Christ. (Gen 3:15, 2 Sam 7:12-17)
Gen 3:15 And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel.
2 Sam 7:12 And when thy days be fulfilled, and thou shalt sleep with thy fathers, I will set up thy seed after thee, which shall proceed out of thy bowels, and I will establish his kingdom. 13 He shall build an house for my name, and I will stablish the throne of his kingdom for ever. 14 I will be his father, and he shall be my son. If he commit iniquity, I will chasten him with the rod of men, and with the stripes of the children of men: 15 But my mercy shall not depart away from him, as I took it from Saul, whom I put away before thee. 16 And thine house and thy kingdom shall be established for ever before thee: thy throne shall be established for ever. 17 According to all these words, and according to all this vision, so did Nathan speak unto David.
The Christ who came according to the prophecy of the Old Testament is Jesus. (Acts 3:20-26, Acts 13:22-23)
Acts 3:20 And he shall send Jesus Christ, which before was preached unto you: 21 Whom the heaven must receive until the times of restitution of all things, which God hath spoken by the mouth of all his holy prophets since the world began. 22 For Moses truly said unto the fathers, A prophet shall the Lord your God raise up unto you of your brethren, like unto me; him shall ye hear in all things whatsoever he shall say unto you. 23 And it shall come to pass, that every soul, which will not hear that prophet, shall be destroyed from among the people. 24 Yea, and all the prophets from Samuel and those that follow after, as many as have spoken, have likewise foretold of these days. 25 Ye are the children of the prophets, and of the covenant which God made with our fathers, saying unto Abraham, And in thy seed shall all the kindreds of the earth be blessed. 26 Unto you first God, having raised up his Son Jesus, sent him to bless you, in turning away every one of you from his iniquities.
Acts 13:22 And when he had removed him, he raised up unto them David to be their king; to whom also he gave their testimony, and said, I have found David the son of Jesse, a man after mine own heart, which shall fulfil all my will. 23 Of this man's seed hath God according to his promise raised unto Israel a Saviour, Jesus:
Also, as proof that Jesus is the Christ, God resurrected Jesus according to the prophecy of the resurrection of Christ in the Old Testament. (Acts 13:34-38)
Acts 13:34 And as concerning that he raised him up from the dead, now no more to return to corruption, he said on this wise, I will give you the sure mercies of David. 35 Wherefore he saith also in another psalm, Thou shalt not suffer thine Holy One to see corruption. 36 For David, after he had served his own generation by the will of God, fell on sleep, and was laid unto his fathers, and saw corruption: 37 But he, whom God raised again, saw no corruption. 38 Be it known unto you therefore, men and brethren, that through this man is preached unto you the forgiveness of sins: