"in an expedient manner," late 14c., from expedient (adj.) + -ly (2).
Entries linking to expediently
expedient adj.
late 14c., "advantageous, fit, proper to a purpose," from Old French expedient "useful, beneficial" (14c.) or directly from Latin expedientem (nominative expediens) "beneficial," present participle of expedire "make fit or ready, prepare" (see expedite). The noun meaning "a device adopted in an exigency, that which serves to advance a desired result" is from 1650s. Related: Expediential; expedientially (both 19c.).
Expedient, contrivance, and device indicate artificial means of escape from difficulty or embarrassment; resource indicates natural means or something possessed; resort and shift may indicate either. [Century Dictionary]
-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.