c. 1300, "matching, similar, corresponding" (a sense now obsolete), present-participle adjective and adverb from accord (v.). Meanings "conforming (to), compliant, in agreement; consistent, harmonious; suitable, appropriate" are from late 14c. According to "referring to," literally "in a manner agreeing with" is from late 14c. As an adverb, "often applied to persons, but referring elliptically to their statements or opinions" [Century Dictionary].
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.
<a href="https://www.etymonline.com/word/accordingly">Etymology of accordingly by etymonline</a>
Harper, D. (n.d.). Etymology of accordingly. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/accordingly