'arch-' originates from Greek, ultimately via Latin/Old French, specifically from Greek 'arkhē' meaning 'rule, chief', used as a prefix meaning 'principal' or 'extreme'; 'humbug' originates in English (early 18th century), of uncertain origin, used to mean 'deceptive talk or behavior'.

'archhumbug' (often written 'arch-humbug') is formed by prefixing English 'arch-' to the native English word 'humbug' in the 19th century to intensify the sense; the compound appears in literary and colloquial usage to mean a supreme humbug or complete imposture.

Initially the parts meant 'chief' (arch-) + 'deception' (humbug), i.e. 'principal deception'; over time the compound came to be used more broadly as 'complete nonsense' or 'a consummate fraud' in modern usage.