From medieval Latin exclūsīvus (= the participial stem of exclūdĕre "to exclude" plus an adjectival ending). (Oxford English Dictionary)
In the sense of exclusive disjunction, the earliest occurrence I have found is in Bradley (1883). Bradley argued that or was unambiguously exclusive. His discussion, like much of the 19th century literature, focused on disjunction of predicates rather than disjunction of propositions:
It has been doubted if alternatives are always exclusive. "A is b or c," it is said, may be taken to admit that A is possibly both. It may either be bc or b or c. And, no doubt, in our ordinary disjunctive statements we either leave the meaning to be gathered from the context, or really may not know what it is that we mean. But our slovenly habits of expression and thought are no real evidence against the exclusive character of disjunction. "A is b or c" does strictly exclude "A is both b and c." When a speaker asserts that a given person is a fool or a rogue, he may not mean to deny that he is both. But, having no interest in showing that he is both, being perfectly satisfied provided he is one, either b or c, the speaker has not the possibility bc in his mind. Ignoring it as irrelevant, he argues as if it did not exist. And thus he may practically be right in what he says, though formally his statement is downright false: for he has excluded the alternative bc. (p. 124)
In the sense of exclusive first-person pronouns, exclusive appears to have been introduced in Humboldt (1828):
Several American languages have two plural forms in the first person, an exclusive and an inclusive form, according as we would include or exclude the person addressed. It has been thought that this peculiarity belonged exclusively to the American languages; but it is also found in the Mantchu, the Tamul, and in all the dialects of the South Sea Islands. All these languages have indeed this grammatical form in common; but it is only in the abstract. Each of them expresses it by a different sound: the identity of this form, therefore, does not furnish any proof of the affinity of these languages. (p. 7)
- Bradley, F.H. (1883) The Principles of Logic. Kegan Paul, Trench and Company.
- von Humboldt, Wilhem (1828) An Essay on the Best Means of Ascertaining the Affinities of Oriental Languages. J.L. Cox.