Josephus is well known to Christian apologists.
In his Antiquity of the Jews (Book i8, Chap. 1, No.2), Josephus states that there were three sects of philosophy amongst the Jews: the Essenes, the Pharisees, and the Sadducees. The doctrine of the Sadducees was that souls die with the bodies, but both the Essenes and the Pharisees, he affirms, believed in rebirth. As to the Essenes, who have now become famous owing to the discovery of the Dead Sea Scrolls, he states elsewhere:
They smiled in their very pains and laughed to scorn those who inflicted torments upon them, and resigned up their souls with great alacrity, as expecting to receive them again.
For their doctrine is this, that bodies are corruptible, and that the matter they are made of is not permanent; but that the souls are immortal, and continue for ever: and that they come out of the most subtile air, and are united to their bodies as to prisons, into which they are drawn by a certain natural enticement; but that when they are set free from the bonds of flesh, they then, as released from a long bondage, rejoice and mount upward. . . .
These are the divine doctrines of the Essenes about the soul....
Jewish War, Book 2, Chap. 8, Nos. 10- 11
[The Pharisees] believe that souls have an immortal vigour in them [and that the virtuous] shall have power to revive and live again: on account of which doctrines they are able greatly to persuade the body of the people.
Antiquity of the Jews, Book i8, Chap. 1, No.3
[From an address of Josephus to some Jewish soldiers who desired to kill themselves rather than be captured by the Romans:]
The bodies of all men are, indeed mortal, and are created out of corruptible matter; but the soul is ever immortal, and is a portion of the divinity that inhabits our bodies. . . . Do ye not remember that all pure Spirits when they depart out of this life obtain a most holy place in heaven, from whence, in the revolutions of ages, they are again sent into pure bodies; while the souls of those who have committed self-destruction are doomed to a region in the darkness of Hades?
Jewish War, Book 3, Chap. 8, No. 5
Flavius Josephus (A.D. 37-100)
More evidence that the Jews definitely believed in reincarnation:
Philo Judeus (20 B.C.-A.D. 54)
Alexandrian Philosopher and Jew
The air is full of souls; those who are nearest to earth descending to be tied to mortal bodies return to other bodies, desiring to live in them.
De Somniis
The company of disembodied souls is distributed in various orders. The law of some of them is to enter mortal bodies and after certain prescribed periods be again set free. But those possessed of a diviner structure are absolved from all local bonds of earth. Some of these souls choose confinement in mortal bodies because they are earthly and corporeally inclined...
All such as are wise, like Moses, are living abroad from home. For the souls of such formerly chose this expatriation from heaven, and through curiosity and the desire of acquiring knowledge they came to dwell abroad in earthly nature, and while they dwell in the body they look down on things visible and mortal around them, and urge their way thitherward again whence they came originally: and call that heavenly region ... their citizenship, fatherland, but this earthly region in which they live, foreign.