The phrase "from the east" (ἀπὸ ἀνατολῶν, apo anatolon), more literally "from the rising [of the sun]," is the only information Matthew provides about the region from which they came. The Parthian Empire, centered in Persia, occupied virtually all of the land east of Judea & Syria (except for the deserts of Arabia to the southeast). Though the empire was tolerant of other religions, its dominant religion was Zoroastrianism. Although Matthew's account does not cite the motivation for their journey, the Syriac Infancy Gospel provides some clarity by stating explicitly in the 3rd chapter that they were pursuing a prophecy from their prophet, Zoradascht (Zoroaster).
