The phenomenon appears to be a result of translation that dates back to early Greek writings. Early works by Greek writers would introduce a topic with Περὶ, meaning about, which Latin scholars translated to De, and were then translated to English as On. The trend of starting essays with On then stuck with English writers, who adopted it in their own titling.
Observation suggests that Περὶ was used to introduce an examination of a subject, such as medicine, grammar, sleep, dreams, etc. Titles by Aristotle that lack this introductory word tend to be those focused on more original concepts, such as Metaphysics (Greek: τὰ μετὰ τὰ φυσικά).
On who titled the works
It's not clear to me whether Aristotle provided titles for his own works, or if they were cataloged by other Greek scholars, particularly the scholars at the Library of Alexandria, where treatises were collected. Several sources, including Encyclopedia Britannica, seem to indicate that the titles were added by Alexandrian scholars, and as such the original titles would have been in Greek, even if they weren't named by Aristotle himself.*
This article from Standford indicates that much of the editorial work related to Aristotle's writings might have been done by Andronicus of Rhodes. Credit to Matt from History.SE for that finding.
Notably, translators used their discretion in applying the original naming to their well-known English names. For example, Aristotle's Poetics is seldom translated in English as On Poetics, though the original Greek is still Περὶ ποιητικῆς, and the Latin is De Poetica.
Another classic example from Aristotle:
- Greek: Περὶ οὐρανοῦ, 350 BC // Latin: De Caelo // English: On the Heavens (Aristotle)
Aristotle was not the first Greek writer to use this style. Writings by Hippocrates have similar titles in Greek.
An example of an English writer adopting the style:
- On Liberty, 1859, John Stewart Mill [credit to WS2 in the comments for pointing to this example]
Additional examples from the Aristotle canon:
Greek: Περὶ Ψυχῆς // Latin: De Anima // English: On the soul
Greek: Περὶ αἰσθήσεως καὶ αἰσθητῶν // Latin: De sensu et sensibilibus // English: On Sense and the Sensible
Greek: Περὶ μνήμης καὶ ἀναμνήσεως // Latin: De memoria et reminiscentia // English: On Memory
*Seeking some added clarity on the origin of the titles of the works, I've posted a question on the History Stack Exchange: Who titled the works of Aristotle?