Old English full "containing all that can be received; having eaten or drunk to repletion; filled; perfect, entire, utter," from Proto-Germanic *fullaz "full" (source also of Old Saxon full, Old Frisian ful, Dutch vol, Old High German fol, German voll, Old Norse fullr, Gothic fulls), from PIE root *pele- (1) "to fill." Related: Fuller; fullest.
The adverb is Old English ful "very, fully, entirely, completely" and was common in Middle English (full well, full many, etc.); sense of "quite, exactly, precisely" is from 1580s. Full moon, one with its whole disc illuminated, was Old English fulles monan; first record of full-blood in reference to racial purity is from 1812. Full house is 1710 in the theatrical sense, 1887 in the poker sense (three of a kind and a pair, earlier full-hand, 1850). Full-dress (adj.) "appropriate to a formal occasion" is from 1761, from the noun phrase.