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.
Related: Exited; exiting.