well (adv.)
"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 *welo- (cognates: 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" (cognates: 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 from 1825.
well (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 *wall- "roll" (cognates: 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, roll" (see volvox), on notion of "roiling or bubbling water."
well (n.)
"hole dug for water, spring of water," Old English wielle (West Saxon), welle (Anglian) "spring of water, fountain," from wiellan (see well (v.)). "As soon as a spring begins to be utilized as a source of water-supply it is more or less thoroughly transformed into a well" [Century Dictionary]. Figurative sense of "source from which anything is drawn" was in Old English.