Now they’re asking you about the Master of the Two Horns. Say to them, “I’ll narrate for you something of his story.” 
The following excerpt is taken from “The Holy Quran in Today’s English” by Yahiya Emerick note 1350:
No record or opinion as to the identity of this figure has survived from the time of the Prophet and his companions. Early commentators were divided among themselves as to which historical figure Dhul Quarnayn could be. However, by the end of the classical period, many commentators, after having been exposed to the stories and legends of Alexander the Great (d. 323 BCE), applied the title to him and were elated that such ‘a great man’ was mentioned in their holy book. Those who still subscribe to this opinion, that Alexander is being spoken of here in verses 83-101, point out that Alexander traveled widely and often wore a pair of ram’s horns on his helmet, a decoration commemorating the Egyptian god Ammon-Ra, which even found its way onto coins minted during the ill-fated ruler’s reign. However, putting these two inconclusive and incidental details aside, could Dhul Quarnayn really be Alexander of Macedon? That question can only be answered by first defining the character of the man mentioned in this chapter and then comparing it with all the available historical accounts that we have of Alexander. Dhul Quarnayn is presented as a pious man who ruled with justice. He also traveled generally west, then generally east and then generally north. Alexander the Great traveled east first, then north, and finally south before going back west, so the chronology of travel doesn’t fit here. This is not the only thing that disqualifies him, however, for Alexander was a polytheist who thought of himself as the son of Zeus! He was also fond of wine, murdered some of his friends and conquered for no other purpose than to be famous forever. (He got what he wanted!) So Alexander doesn’t fit very well with the description of Dhul Quarnayn. So who was Dhul Quarnayn, or the Master of the Two Horns? It was the Jews of Medina who had suggested to the Meccans that they ask Muhammad this question. This story was revealed in response. A Persian king named Cyrus the Great (d. 529 BCE) is the definitve candidate, and the proof is very convincing. If we remember the origin of the question that the Meccans put to the Prophet, that it came from the Jews of Medina, and if we also remember that every other similar question the Jews proposed originated from their religion, historical experience and their scripture, then we need do no more than look to the Jewish scriptures for the source of the reference. The Jewish prophet Daniel, who was living in captivity in Babylon, saw a vision of a ram with two horns of different heights. (Thousands of Jews, including Daniel, had been forcibly relocated from Israel to Babylon by the Babylonian tyrant Nebuchadnezzar many years before.) Then Daniel saw a goat (in his vision) with one small horn breaking the two horns of the ram, and then the goat’s horn broke into four pieces in turn. According to Daniel, Angel Gabriel came and explained the meaning of the vision. It was that the nations of the Medes and the Persians (symbolized as two horns) would unite to make a great empire spanning a huge territory (under Cyrus’s rule) and further that a Greek king, (Alexander the Great,) would then vanquish that empire, and in turn his kingdom would break up into four smaller kingdoms. (See Daniel 8:1-22) In Daniel’s lifetime, the Babylonians were in fact defeated by Cyrus the Great, the first king and uniter of the Medes and the Persians (see Daniel 5:30-31), and on a map Cyrus’s empire looks roughly like two horns arcing up to the east and west with Persia as the epicenter, while the eastern half of his empire arcs up further north than the western half. (As Biblical scholars admit, the book of Daniel erroneously rearranges the chronology of the two Persian kings, Cyrus and Darius I and mistakenly identifies Darius I, the third reigning Persian king, as the first Persian king and conqueror of the Babylonians. Ezra 4:3-5, however, gets the chronology right.) Cyrus the Great has been beloved of Jews ever since that time on account of the fact that he let the Jewish captives return home to Israel. He is also revered by Jews as having been a righteous man, devoted to God, (see Daniel 6:26-28) and the renovator of many holy places in Jerusalem. Thus, Dhul Quarnayn can be none other than Cyrus the Great of Persia, as the Jews knew him to be the meaning of the vision of the master of the two ram’s horns. (Ma’ariful Qur’an, Tafhimul Qur’an)
Emerick, Yahiya. The Meaning of the Holy Qur’an in Today’s English (p. 827). Unknown. Kindle Edition.