Unlike every other holiday of the year, Simchat Torah is a holiday that has no biblical basis. All the other holidays celebrate a harvest (Sukkot, Pesach, Shavuot), a historical event (Chanukah, Purim, Pesach, the fast days), or a religious observance (Rosh Hashanah, Yom Kippur, Shemini Atzeret).
Simchat Torah as a holiday evolved out of the events that marked the end of the Torah-reading cycle.
The custom of reading the Torah publicly, which began after the return from Babylonian exile, did not become a fixed ritual until some time after the third century CE, so there was no particular date when the entire Torah’s reading was completed and begun anew. The custom of marking the reading of the end of Deuteronomy with a celebration was known in Babylon during the gaonic period (ca. 590–1000 CE), when the reading of the Torah was fixed on a one-year cycle, but these celebrations were not the origin of the Simchat Torah holiday.
In Babylon during the gaonic period, the Torah had been divided into 54 parashiot, “reading portions,” with one (or two during the shorter non-leap years) to be read each Shabbat during the year. The day that the last portion of Deuteronomy was read was called Yom haBrakha after the name of the parashah, v’Zot haBrakha. Some communities, particularly those in northern Africa, called it Yom haSiyyum, the “Day of Completion,” while in Spain it didn’t have any name in particular, it was just referred to as the last yom tov of Chag.
Development of the Simchat Torah celebration into its modern form seems to have occurred slowly, over the course of several centuries. Until the eleventh century the holiday continued to be known as the second day of Shemini Atzeret or even, as in Spain, as the ninth day of Sukkot. It appears that the first use of the holiday name of “Simchat Torah” occurred in Spain some time during the late eleventh century.
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