Actually, there's no source for this story at all, save a desire to believe that the ordering of books within Tanakh was deliberate, rather than simply retroactive. The gemara (Bava Batra 15a-b) speaks of the order in which the books appear and of their composition, while the mishna (Yadayim 3:6) possibly alludes to a debate that concerned the scriptural status of Shir haShirim and Qohelet. Elsewhere, intimations exist that concern the potential illegitimacy of Ezekiel as a scriptural text (Shabbat 13b), as well as the potential legitimacy of Ben Sirakh and Megillat Taanit.
The first person to suppose that a council once existed at which the Tanakh was finalised was Heinrich Graetz in his 1871 "Der alttestamentliche Kanon und sein Abschluss". This theory may have some merit or it may not; either way, it was a fabrication, invented to make sense of the evidence that does exist.
The supposition that the Tanakh was finalised several centuries earlier by the Anshei Kenesset haGedolah also makes sense - but only if you choose to believe that the Tanakh was already in its final form at the time of the Mishna's composition. Since the Mishna never says that it was, whether or not you believe it to have been is entirely up to you.
In order to better appreciate why it's not strange that it wouldn't be, consider that the Tanakh did not appear in codex form (in Hebrew, that is) until the 10th century. During the period of which we are speaking, the "Tanakh" was just a collection of individual scrolls. Knowing what was "in" the Tanakh and what was not meant knowing which of those scrolls were scripturally authoritative and which were not.