"in an exact manner, with minute correctness," 1530s, from exact (adj.) + -ly (2). Elliptical use for "quite right" not recorded before 1869.
Entries linking to exactly
exact adj.
"precise, rigorous, accurate," 1530s, from Latin exactus "precise, accurate, highly finished," past-participle adjective from exigere "demand, require, enforce," literally "to drive or force out," also "to finish, measure," from ex "out" (see ex-) + agere "to set in motion, drive, drive forward; to do, perform" (from PIE root *ag- "to drive, draw out or forth, move").
-ly 2
common adverbial suffix, forming from adjectives adverbs signifying "in a manner denoted by" the adjective, Middle English, from Old English -lice, from Proto-Germanic *-liko- (cognates: Old Frisian -like, Old Saxon -liko, Dutch -lijk, Old High German -licho, German -lich, Old Norse -liga, Gothic -leiko); see -ly (1). Cognate with lich, and identical with like (adj.).
Weekley notes as "curious" that Germanic uses a word essentially meaning "body" for the adverbial formation, while Romanic uses one meaning "mind" (as in French constamment from Latin constanti mente). The modern English form emerged in late Middle English, probably from influence of Old Norse -liga.