Question:

I would like to know where it is written in the Torah that we should await and yearn for the arrival of a leader who will be the Moshiach.

Response:

There are many verses in the Torah (you can see some of them in this list of source texts) which predict the coming of Moshiach. None of them state explicitly, “Thou shalt await the arrival of Moshiach every day!” Nevertheless, hundreds of commands throughout the Torah are screaming just that.

What do I mean? The Torah gives us 613 mitzvot to do. Many of these mitzvot are to be done in the Temple in Jerusalem. Others are applicable only when all or most of the Jewish people are living in the Jewish land. Altogether, the majority of these mitzvot cannot be fulfilled as long as we as a nation are scattered all over the Diaspora and there is no Temple in Jerusalem—and the only way that this can be repaired is through the promised leader and sage to whom we refer as the Moshiach.

So you see that every one of these unfulfilled mitzvot is silently screaming, “Bring the Moshiach so that you can fulfill me! I know that Moshiach will once again build the Temple, so that I will be revived!”

And if so, should not the heart of a sensitive Jew cry and yearn in the same way?