In his defense of Judaism against Apion, Josephus writes about the Jewish Scriptures, comparing their fixed canon with the multitude of Greek books. He defined the Hebrew canon as containing twenty-two books, dividing the Scriptures into three main sections, but differently from the standard Jewish divisions.
His first group were the five books of Moses, covering a period of three thousand years from creation to Moses.
The second group were thirteen books of prophets from Moses to the Persian king, Artaxerxes. These would probably have been Joshua, Judges and Ruth combined, Samuel, Kings, Isaiah, Jeremiah and Lamentations combined, Ezekiel, twelve minor prophets, Job, Daniel, Esther, Ezra and Nehemiah combined and Chronicles.
The last were the remaining four books of hymns and precepts (Psalms, Proverbs, Ecclesiastes and Song of Solomon).
According to Josephus, the last scriptures written under God's inspiration were from the time of Artaxerxes, king of Persia (465 - 424 BC), this would be the Book of Malachi. Ezra arrived in Jerusalem in the seventh year of Artaxerxes (Ezra 7:8), and Nehemiah arrived in the twentieth year (Neh 2:1). This would indicate that the Hebrew Scriptures were considered complete from around 440 BC. Josephus was writing around AD 90, so he confirms that there was no Word from God throughout the inter-testamental period.
Josephus: Against Apion 1.8
8. For we have not an innumerable multitude of books among us, disagreeing from and contradicting one another, [as the Greeks have,] but only twenty-two books, which contain the records of all the past times; which are justly believed to be divine; and of them five belong to Moses, which contain his laws and the traditions of the origin of mankind till his death. This interval of time was little short of three thousand years; but as to the time from the death of Moses till the reign of Artaxerxes king of Persia, who reigned after Xerxes, the prophets, who were after Moses, wrote down what was done in their times in thirteen books. The remaining four books contain hymns to God, and precepts for the conduct of human life. It is true, our history hath been written since Artaxerxes very particularly, but hath not been esteemed of the like authority with the former by our forefathers, because there hath not been an exact succession of prophets since that time; and how firmly we have given credit to these books of our own nation is evident by what we do; for during so many ages as have already passed, no one has been so bold as either to add any thing to them, to take any thing from them, or to make any change in them; but it is become natural to all Jews immediately, and from their very birth, to esteem these books to contain Divine doctrines, and to persist in them, and, if occasion be willingly to die for them. For it is no new thing for our captives, many of them in number, and frequently in time, to be seen to endure racks and deaths of all kinds upon the theatres, that they may not be obliged to say one word against our laws and the records that contain them; whereas there are none at all among the Greeks who would undergo the least harm on that account, no, nor in case all the writings that are among them were to be destroyed; for they take them to be such discourses as are framed agreeably to the inclinations of those that write them; and they have justly the same opinion of the ancient writers, since they see some of the present generation bold enough to write about such affairs, wherein they were not present, nor had concern enough to inform themselves about them from those that knew them; examples of which may be had in this late war of ours, where some persons have written histories, and published them, without having been in the places concerned, or having been near them when the actions were done; but these men put a few things together by hearsay, and insolently abuse the world, and call these writings by the name of Histories.