late 14c., intransitive and transitive, "come next after, follow after another; take the place of another, be elected or chosen for" a position, from Old French succeder "to follow on" (14c.) and directly from Latin succedere "come after, follow after; go near to; come under; take the place of," also "go from under, mount up, ascend," hence "get on well, prosper, be victorious," from sub "next to, after" (see sub-) + cedere "go, move" (from PIE root *ked- "to go, yield").
Meaning "to continue, endure" is from early 15c. The sense of "turn out well, have a favorable result" in English is first recorded late 15c., with ellipsis of adverb (succeed well). Of persons, "to be successful," from c. 1500. Related: Succeeded; succeeding.