How did the "wise men" become known as 3 kings? In Matt 2, the men from east who came to visit Baby Jesus are referred to as wise men. 

However, now they are also known as three kings. When did they become known as "kings" rather than "wise men" and what is the basis for the description? 

Additionally, they are often referred to as the 3 magi. What is the basis for each of these descriptors?
It is mentioned from The Catholic Encyclopedia website:
In reference to there being three kings:

No Father of the Church holds the Magi to have been kings. Tertullian
(&quot;Adv. Marcion.&quot;, III, xiii) says that they were wellnigh kings (fere
reges), and so agrees with what we have concluded from non-Biblical
evidence. The [Catholic] Church, indeed, in her liturgy, applies to the Magi the
words: &quot;The kings of Tharsis and the islands shall offer presents; the
kings of the Arabians and of Saba shall bring him gifts: and all the
kings of the earth shall adore him&quot; (Psalm 71:10). But this use of the
text in reference to them no more proves that they were kings than it
traces their journey from Tharsis, Arabia, and Saba.
...
[About there being three]
Among the Latins, from the seventh century, we find slight variants of
the names, Gaspar, Melchior, and Balthasar; the Martyrology mentions
St. Gaspar, on the first, St. Melchior, on the sixth, and St.
Balthasar, on the eleventh of January.

Another reason that there are traditionally Three wise men / Magi is because there were three gifts brought (Gold, Frankincense, Myrrh).
It should also be considered, the significance of the number three in scripture:

In some cases the number three may signify completeness or finality. Thus Pope observes that the number three “naturally suggests the idea of completeness—beginning, middle, end.”34 Beyond this natural expectation, however, is the realization that “the figure three is an evocative image, filled with connotations” so that “three consecutive occurrences of an event serves as a rhetorical signal indicating special significance.