1530s, from Latin exit "he or she goes out," third person singular present indicative of exire "go out," from ex- "out" (see ex-) + ire "to go" (see ion).
Also from Latin exitus "a leaving, a going out," noun of action from exire. Originally in English a Latin stage direction (late 15c.); sense of "door for leaving" is 1786. Meaning "departure" (originally from the stage) is from 1580s. The verb is c.1600, from the noun; it ought to be left to stage directions and the clunky jargon of police reports.
Those who neither know Latin nor read plays are apt to forget or not know that this is a singular verb with plural exeunt. [Fowler]Related: Exited; exiting.