In Against Apion 1:38-43 (probably written in the early second century), Josephus wrote the following:
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 has been written since Artaxerxes very particularly, but has not been esteemed of the like authority with the former by our forefathers, because there has 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 anything to them, to take any thing from them, or to make any change in them; but it is becomes 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.
This passage is of great importance, as it shows that, for Josephus and the Jews of his era, the authoritative set of books (“canon” to use an anachronistic term) did not include the Apocrypha (Deutero-canon in Catholic circles), such as 1-2 Maccabees; instead, they held to the non-Catholic/Eastern Orthodox canon.
In Antiquities of the Jews, an earlier work, Josephus mentions that these books alone were laid up in the temple:
But they were astonished at this wonderful effect, and, as it were, quenched their thirst by the very sight of it. So they drank this pleasant, this sweet water; and such it seemed to be, as might well be expected where God was the donor. They were also in admiration how Moses was honoured by God; and they made grateful returns of sacrifices to God for his providence toward them. Now that Scripture, which is laid up in the temple, informs us, how God foretold to Moses, that water should in this manner be derived out of the rock. (Antiquities 3:38)
Some may wonder why the Old Testament that Latter-day Saints, Protestants, and others hold to are composed of 39 books, but Josephus mentions 22. The answer is that, for Jews, the Five Books of Moses were one “book” (scroll); 1-2 Samuel; 1-2 Kings; 1-2 Chronicles; Ruth-Judges; Ezra-Nehemiah; Jeremiah-Lamentations; and the Twelve Minor Prophets were each one book/scroll. Overall, the “magic number” would be either 22 or 24. Notwithstanding, there is clearly no room for the stand-alone books that the Council of Trent would, in the Catholic perspective, infallibly define as canonical in April 1546.
A very good article on Josephus' Old Testament canon would be that of:
Duane L. Christensen, Josephus and the Twenty-Two Book Canon of Sacred Scripture, JETS 29/1 (March 1986): 37-46 (pdf)
Christensen concludes his article as follows:
In short, the canon of Josephus is essentially that of the Masoretic tradition with one important modification. The festal scrolls, or at least an earlier form of them that did not include Esther, constituted a single canonical category within a collection of twenty-two books. By choosing the number of letters of the Hebrew alphabet as a structuring principle, those early scribes also effectively closed their canon. The only way for later works to make it into the collection was for them to be incorporated within existing canonical categories or to transform the very structure of the canon itself. This transformation apparently was accomplished first with the inclusion of Esther to form the Talmudic canon of twenty-four books, and again within the Christian community by the addition of the NT.
The early Jewish rejection of the inspired nature of the Apocrypha, as evidenced by Josephus among other witnesses (including a number of early Christian authors even up until the Council of Trent itself [not just Jerome]) supports the Latter-day Saint rejection of the Apocrypha/Deutero-canonical books, based on D&C 91, a revelation given to the Prophet Joseph Smith in 1833.
