The answer isn't a single source but a combination of multiple sources.
First, the Talmud in Bava Basra 14b-15a lists the authors and editors of each book of Tanach. The Anshei Kneses HaGedolah are the latest-in-time group to participate in writing/editing any sefer in Tanach.
Second, Ben Sira's grandson--in his introduction to Sefer Ben Sira--refers to Torah, Neviim, and "others" as three categories of scripture. This implies that at least the first two categories were already fixed as of the middle of the Second Temple and that there was a distinct--albeit unnamed--third category.
Third, Josephus--writing at the end of the Second Temple period in Contra Apion 1:8--writes as point of pride that the Jewish books are limited to those believed to be divine and that they trace Jewish history until the reign of Artaxerxes, the time when the last writers lived. This is the early part of the Second Temple era, same time as the Anshei Knesses HaGedolah lived. (Although Josephus states there are 22 books, it seems clear that he is combining some of the non-historical books--perhaps Shir Hashirim/Koheles/Mishlei--becomes he says explicitly that there are 13 post-Moses historical books, which is the same number we have). Josephus is clearly describing what we would call a Canon.
In summary, we have a source that the Anshei Knesses HaGedolah participated in the writing/editing of some of the later books of Tanach. We have an indication from the middle of the Second Temple Era that the category of Neviim was already fixed. And we have Josephus describing a canon that was last added to--at least with respect to historical works--at the time of the Anshei Knesses HaGedolah.