This is a very complicated topic that is full of popular speculation, which I will exemplify below. My understanding is that there is no one underlying cause for the religion's "transition" into monotheism (by technicality, "Judaism" was never anything but monotheistic – the right question is, how did the ancient Israelite religion's lead to a monotheistic Judaism?. There are however, interesting texts and major influences that may be worth looking into.

There are many suppositions and a lot of conjecture about Judaism's (specifically its antecedent, ancient Israelite religions) pre-monotheistic history (i.e. in its polytheistic/henotheistic discipline) and where it mostly derives its influences.

On the topic of popular speculation, look at the subject of Yahweh (Jehova) and Asherah, for instance. You might have heard of Yahweh, and his consort Asherah. Historically speaking, the idea of Asherah and her role is mostly speculative (especially in regard to her equitability to Yahweh at the time), but there is reason behind the speculation about Asherah's role that makes her a popular point concerning pre-Judaism (or rather, Yahwist) and its world of "henotheism/polytheism."

A second important primary source for YHWH's status in Judah is one of the Khirbet el-Qom inscriptions dating between 800-750 BCE. It mentions "YHWH and his Asherah," indicating that Judah's supreme god YHWH had a paredra ("sacred consort"). This indication of the cult of Asherah as paredra of YHWH can be connected with the HB references to the cult of the "Queen of Heaven" in Jerusalem.

Herbert Niehr, "The Rise of YHWH in Judahite and Israelite Religion: Methodological and Religio-Historical Aspects" from The Triumph of Elohim: From Yahisms to Judaisms by Diana Vikander Edelman

This is a popular example of one of the subjects that treads on the line of oversimplification and hyperbole, that is simply speculative and conjectural.

Moreover, on monotheism, and in relevance to /u/darkekniggit's question, "Follow up. Is there anything known about the precursor faiths to Judaism if there are any?"

This is where ancient Iran's Zoroastrianism, and ancient Egypt's Akhenaten play a part, but this topic has been discussed before on this subreddit.

I would read about Zoroastrianism's influence on Judaism's monotheism here. (Kaufmann Kohler, A. V. W. Jackson. "Zoroastrianism.") (Also, you should read this post about Zoroastrianism and its relevance to Judaism.)

Other general posts which cover this topic are this and this.