Old English *willan, wyllan "to wish, desire; be willing; be used to; be about to" (past tense wolde), from Proto-Germanic *willjan (source also of Old Saxon willian, Old Norse vilja, Old Frisian willa, Dutch willen, Old High German wellan, German wollen, Gothic wiljan "to will, wish, desire," Gothic waljan "to choose").
The Germanic words are from PIE root *wel- (2) "to wish, will" (source also of Sanskrit vrnoti "chooses, prefers," varyah "to be chosen, eligible, excellent," varanam "choosing;" Avestan verenav- "to wish, will, choose;" Greek elpis "hope;" Latin volo, velle "to wish, will, desire;" Old Church Slavonic voljo, voliti "to will," veljo, veleti "to command;" Lithuanian velyti "to wish, favor," pa-velmi "I will," viliuos "I hope;" Welsh gwell "better").
Compare also Old English wel "well," literally "according to one's wish;" wela "well-being, riches." The use as a future auxiliary was already developing in Old English. The implication of intention or volition distinguishes it from shall, which expresses or implies obligation or necessity. Contracted forms, especially after pronouns, began to appear 16c., as in sheele for "she will." In early use often -ile to preserve pronunciation. The form with an apostrophe ('ll) is from 17c.