c. 1200, "year-day, annual return of a certain date in the year," originally especially of the day of a person's death or a saint's martyrdom, from Medieval Latin anniversarium, noun from Latin anniversarius (adj.) "returning annually," from annus (genitive anni) "year" (see annual (adj.)) + versus, past participle of vertere "to turn" (from PIE root *wer- (2) "to turn, bend").
The adjective came to be used as a noun in Church Latin via anniversaria dies in reference to saints' days. Anniversary as an adjective in English is from mid-15c. An Old English word for "anniversary" (n.) was mynddæg, literally "mind-day."