The story of Daniel is fulfillment of the prophecy in Isaiah chapter 39. Thus Daniel sits in slot 39 of the book order as the last book of the Old Testament. That Daniel is the end of the Old Testament is curious considering it's regularly studied in tandem with Revelation, the last book of the New Testament.
There are several matches between Isaiah 39 and Daniel, but the passages do not lend themselves to quoting in small bits so I've just provided two longer quotes and followed up with notes below.
1At that time Merodach-Baladan, the son of Baladan, king of Babylon, sent letters and presents to Hezekiah; for he had heard that he had been sick and was healed.
2And Hezekiah was glad to receive them, and showed them his treasure house, the silver and the gold and the spices and the precious ointment and all the house of his armor and all that was found in his treasures; there was nothing in his house nor in all his dominion that Hezekiah did not show them.
3Then Isaiah the prophet came to King Hezekiah and said to him, What did these men say to you? Where did they come to you from? And Hezekiah said, They have come to me from a far country, even from Babylon.
4Then he said, What have they seen in your house? And Hezekiah answered, They have seen all the things that are in my house; I have left nothing in my house that I have not shown them.
5Then Isaiah said to Hezekiah, Hear the word of Yahvah of hosts,
6Look, the days are coming, when all that is in your house, and what your fathers have laid up in store to this day, will be carried to Babylon; nothing will be left says Yahvah.
7And some of your sons that will issue from you, whom you will beget, they will take away; and they will be eunuchs in the house of the king of Babylon.
8Then Hezekiah said to Isaiah, Good is the word of Yahvah which you have spoken. For there will be peace and truth in my days.
1In the 3rd year of the reign of Jehoiakim, king of Judah, Nebuchadnezzar, king of Babylon, came to Jerusalem, and besieged it.
2And master delivered it into his hand, together with Jehoiakim, king of Judah, and the vessels of the house of Yahvah, which he carried away into the land of Shinar, to the house of his idol; and he brought the vessels into the treasure house of his idol.
3And the king spoke to Ashpenaz the chief of the eunuchs, that he should bring some of the sons of Israel, of the royal seed, and of the Parthians;
4boys in whom was no blemish, who were handsome in their appearance and skillful in all wisdom and cunning in knowledge and understanding of science, those who were able to stand in the king's house to minister to him, and whom they might teach the learning and the language of the Chaldeans.
One of the obvious matches beween Isaiah 39 and Daniel is the theme of Babylon. Hezekiah is visited by envoys from Babylon and is given a word that his kingdom is eventually going there. Daniel begins with people and treasures and all being hauled to Babylon. So the word was fulfilled.
Something you don't know from reading the book of Daniel or anywhere else in Scripture is that Daniel is a descendent of Hezekiah. You know from reading the book of Daniel that Daniel had been in the royal court, but that alone does not prove his lineage back to Hezekiah. With Daniel and Isaiah 39 matched it's clear that at least Daniel is in view when God spoke to Hezekiah about his descendents.
Hezekiah is told that his sons would become eunuchs in Babylon. It's not in the Daniel quote above, but if you read further in Daniel chapter 1, Daniel and his friends are in the care of a guy who is chief of the eunuchs. That means Daniel was a eunuch in Babylon and a second aspect of the word Isaiah spoke is fulfilled in Daniel's story.
The other matching component that's in both passages is this theme of treasures. Hezekiah was not discrete with his treasures and so the word came from Yahvah that those treasures would eventually be taken to Babylon. The book of Daniel begins with the story of some of the temple articles and other treasures being taken to Babylon. So the word came true on this third point also.
All in all it's quite clear we're looking at Daniel when we read Isaiah 39.