One of the foundations of Judaism is to believe in the coming of the messiah and to await his arrival, without predicting a particular time for it.

Believing that he will come:

The twelfth principle is that of the messianic era. This requires us to believe and trust that the messiah will come, and not think that he will come too late: “If it tarries, wait for it” (Habakkuk 2:3). We may not designate a [specific] time for his arrival, nor conjecture based on biblical verses to deduce when it will occur. The Sages say, “May those who calculate the end of days be cursed” (Sanhedrin 97b).

Believing that he will be greater than all kings who have preceded him, and that he is descended from the house of David:

We must believe that the messiah will be superior to, and more illustrious than, all other kings in history, as we see in the prophecies of all the prophets from Moses to Malakhi. One who has doubts about him or diminishes his stature rejects the Torah…This principle also includes the belief that the king of Israel may come only from the house of David, descended from Solomon. Anyone who opposes this family has rejected God and the words of His prophets. (Rambam, Commentary on the Mishna, Sanhedrin 10:1)

Further reading: For more on the coming of the messiah, see A Concise Guide to the Sages, p. 391.

Belief in the coming of the messiah stems from belief in the prophetic texts, which itself is a Torah commandment. Nevertheless, one who does not believe in his coming, but does believe in divine reward and punishment of another kind, is not considered as one who rejects a fundamental principle of the Torah.

Belief in the messiah stems from belief in the prophetic texts:

Faith in the coming of the messiah is incumbent on all who accept the Torah of Moses. This is because the obligation to believe the statements of the prophets is explicitly stated in the Torah: “him you shall heed” (Deuteronomy 18:15), and the prophets spoke about the coming of the messiah. It is therefore clear that anyone who does not believe in his coming rejects the statements of the prophets and has violated a Torah commandment.

The importance of belief in divine reward and punishment:

Nevertheless, belief in the coming of the messiah is not a principle that amounts to a rejection of the entire Torah if one does not subscribe to it. Belief in [divine] reward is essential for every believing Jew and rejecting this principle is equivalent to rejecting the foundation of belief in God. Yet if one believes that reward is only for souls in the World to Come, or that it is physical, and [relates] to the resurrection of the dead, then even if he does not believe that there is [divine] reward in this world, he has not rejected the foundation, because he believes in the general principle of reward and punishment, although he disputes one type of reward. (Rav Yosef Albo, Sefer HaIkkarim 4:42)