"brought to a full or completed state," 1746, past-participle adjective from round (v.).
"to spring, rise, gush," Old English wiellan (Anglian wællan), causative of weallan "to boil, bubble up, rise (in reference to a river)" (class VII strong verb; past tense weoll, past participle weallen), from Proto-Germanic *wellanan "to roll" (source also of Old Saxon wallan, Old Norse vella, Old Frisian walla, Old High German wallan, German wallen, Gothic wulan "to bubble, boil"), from PIE root *wel- (3) "to turn, revolve," on notion of "roiling or bubbling water."
"in a satisfactory manner," Old English wel "abundantly, very, very much; indeed, to be sure; with good reason; nearly, for the most part," from Proto-Germanic *wel- (source also of Old Saxon wela, Old Norse vel, Old Frisian wel, Dutch wel, Old High German wela, German wohl, Gothic waila "well"), from PIE root *wel- (2) "to wish, will" (source also of Sanskrit prati varam "at will," Old Church Slavonic vole "well," Welsh gwell "better," Latin velle "to wish, will," Old English willan "to wish;" see will (v.)).
Also used in Old English as an interjection and an expression of surprise. The adjective was in Old English in the sense "in good fortune, happy," from the adverb; sense of "satisfactory" is from late 14c.; "agreeable to wish or desire" is from mid-15c.; "in good health, not ailing" is from 1550s. Well-to-do "prosperous" is recorded by 1794.