The composition of the Torah (or Pentateuch, the first five books of the Hebrew Bible—Genesis, Exodus, Leviticus, Numbers, and Deuteronomy) was a process that involved multiple authors over an extended period of time.

Jewish tradition held that all five books were originally written by Moses in the 2nd millennium BCE, but since the 17th century modern scholars have rejected Mosaic authorship. The precise process by which the Torah was composed, the number of authors involved, and the date of each author remain hotly contested. Some scholars, such as Rolf Rendtorff, espouse a fragmentary hypothesis, in which the Pentateuch is seen as a compilation of short, independent narratives, which were gradually brought together into larger units in two editorial phases: the Deuteronomic and the Priestly phases. By contrast, scholars such as John Van Seters advocate a supplementary hypothesis, which posits that the Torah is the result of two major additions—Yahwist and Priestly—to an existing corpus of work. Other scholars, such as Richard Elliott Friedman or Joel S. Baden, support a revised version of the documentary hypothesis, holding that the Torah was composed by using four different sources—Yahwist, Elohist, Priestly, and Deuteronomist—that were combined into one in the Persian period in Yehud.

Scholars frequently use these newer hypotheses in combination, making it challenging to classify contemporary theories as strictly one or another. The general trend in recent scholarship is to recognize the final form of the Torah as a literary and ideological unity, based on earlier sources, was likely completed during the Persian period (539–333 BCE).

Classical source criticism seeks to determine the date of a text by establishing an earliest possible date (terminus post quem) and a latest possible date (terminus ante quem) on the basis of external attestation of the text's existence, as well as the internal features of the text itself. On the basis of a variety of arguments, modern scholars generally see the completed Torah as a product of the time of the Persian Achaemenid Empire (probably 450–350 BCE), although some would place its composition in the Hellenistic period (333–164 BCE).

Concrete archaeological evidence bearing on the dating of the Torah is found in early manuscript fragments, such as those found among the Dead Sea Scrolls. The earliest extant manuscript fragments of the Pentateuch date to the late third or early second centuries BCE. In addition, early non-biblical sources, such as the Letter of Aristeas, indicate that the Torah was first translated into Greek in Alexandria under the reign of Ptolemy II Philadelphus (285–247 BCE). These lines of evidence indicate that the Torah must have been composed in its final form no later than c. 250 BCE, before its translation into Greek.

There is one external reference to the Torah which, depending on its attribution, may push the terminus ante quem for the composition of the Torah down to about 315 BCE. In Book 40 of Diodorus Siculus's Library, an ancient encyclopedia compiled from a variety of quotations from older documents, there is a passage that refers to a written Jewish law passed down from Moses. Scholars have traditionally attributed the passage to the late 4th-century Greek historian Hecataeus of Abdera, which, if correct, would imply that the Torah must have been composed in some form before 315 BCE. However, the attribution of this passage to Hecataeus has been challenged recently. Russell Gmirkin has argued that the passage is in fact a quote from Theophanes of Mytilene, a first-century BCE Roman biographer cited earlier in Book 40, who in turn used Hecataeus along with other sources. Lester Grabbe considers Gmirkin's arguments unconvincing.

The Elephantine papyri show clear evidence of the existence c. 400 BCE of a polytheistic Judean colony in Egypt who show no knowledge of a written Torah or the narratives described therein. The papyri also document the existence of a small Jewish temple at Elephantine, which possessed altars for incense offerings and animal sacrifices, as late as 411 BCE. Such a temple would be in clear violation of Deuteronomic law, which stipulates that no temple may be constructed outside of Jerusalem. Furthermore, the papyri show that the Jews at Elephantine sent letters to the high priest in Jerusalem asking for his support in rebuilding their local temple, which seems to suggest that the priests of the Second Temple were not enforcing Deuteronomic law at that time.

A minority of scholars such as Niels Peter Lemche, Philippe Wajdenbaum, Russell Gmirkin, and Thomas L. Thompson have argued that the Elephantine papyri demonstrate that monotheism and the Torah could not have been established in Jewish culture before 400 BCE, and that the Torah was therefore likely written in the Hellenistic period, in the third or fourth centuries BCE (see § Possibility of a Hellenistic origin). By contrast, most scholars explain this data by theorizing that the Elephantine Jews represented an isolated remnant of Jewish religious practices from earlier centuries, or that the Torah had only recently been promulgated at that time.