"intentionally, by design," late 15c., from purpose (n.) + -ly (2).
Entries linking to purposely
purpose n.
c. 1300, purpus, "intention, aim, goal; object to be kept in view; proper function for which something exists," from Anglo-French purpos, Old French porpos "an aim, intention" (12c.), from porposer "to put forth," from por- "forth" (from a variant of Latin pro- "forth;" see pur-) + Old French poser "to put, place" (see pose (v.1)).
Etymologically it is equivalent to Latin propositium "a thing proposed or intended," but evidently formed in French from the same elements. From mid-14c. as "theme of a discourse, subject matter of a narrative (as opposed to digressions), hence to the purpose "appropriate" (late 14c.). On purpose "by design, intentionally" is attested from 1580s; earlier of purpose (early 15c.).
-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.