The new covenant was prophesied in Jeremiah 31:
Behold, the days are coming, says the LORD, when I will make a new covenant with the house of Israel and the house of Judah, not like the covenant which I made with their fathers when I took them by the hand to bring them out of the land of Egypt, my covenant which they broke, though I was their husband, says the LORD. But this is the covenant which I will make with the house of Israel after those days, says the LORD: I will put my law within them, and I will write it upon their hearts; and I will be their God, and they shall be my people . . . [and] I will forgive their iniquity, and I will remember their sin no more.