mid-15c., "commonly," from famous + -ly (2). From 1570s as "with celebrity;" from c. 1600 in colloquial sense "remarkably well."
Entries linking to famously
famous adj.
late 14c., "celebrated in public report, renowned, well-known" also "notorious, infamous," from Anglo-French famous, Old French fameus (Modern French fameux), from Latin famosus "much talked of, renowned," often "infamous, notorious, of ill repute," from fama (from PIE root *bha- (2) "to speak, tell, say"). A native word for this was Old English namcuð, literally "name-known." Catch phrase famous last words in the humorous sense "remark likely to prove fatally wrong" is attested from 1921 (early lists of them include "Let's see if it's loaded ... We'll get across before the train comes ... Which one is the third rail? ... Light up, it can't explode").
-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.