The start of that special feast goes back to the 1920, and is connected to the then-only BG University - the Sofia University St Kliment Ohridski. Article 25 of the General Regulations of the University, dated 1905, said: November 25th (new style: Dec. 8th), the Day of St Kliment Ohridski, and Feast Day of the University - official promotion of the new Rector. The old Rector gives a speech for University progress, and then the new one gives an academic speech. That is considered to be the official beginning of the December 8th Students' Feast celebrations.
After 1944, when the communists took over in Bulgaria, that feast was cancelled and was replaced with the International Students' Solidarity Day: November 17th. Fortunately, the Students' Feast Day was restored in 1962, and has been celebrated each year ever since.