An EU invention that apparently became canon. Probably as far back as the WEG RPG or the introduction of Carida in the Jedi Academy Trilogy.
I prefer to think that the Academy predates the Empire by millennia, like some old world university (e.g. Oxford), but has sector-level branches of varying prestige throughout the galaxy so even kids from backwaters like Tatooine can attend.
But that's just me.