1530s (late 15c. as a Latin word in English), originally a stage direction, from Latin exit "he or she goes out," third person singular present indicative of exire "go out, go forth, depart," from ex- "out" (see ex-) + ire "to go" (from PIE root *ei- "to go"). Also from Latin exitus "a leaving, a going out," noun of action from exire.
Meaning "a departure" (originally from the stage) is from 1580s. Meaning "a way of departure" is from 1690s; specific meaning "door for leaving" is from 1786. 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.
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]
Exit poll attested by 1980.