'archmagician' is formed from the prefix 'arch-' and the word 'magician'; 'arch-' originates from Greek, specifically the word 'arkhos' (or 'arkhē/arkhos'), where 'arkhos' meant 'chief' or 'principal', and 'magician' originates from Late Latin 'magicus' via Old French 'magicien', ultimately from Greek 'magos' and Old Persian 'maguš'.

'arch-' entered English as a combining prefix from Greek 'arkhos' (via Latin 'archi-'); 'magician' changed from Old French 'magicien' and Latin 'magicus' into Middle English 'magicien' and eventually modern English 'magician'; the compound 'archmagician' is a Modern English formation combining these elements to denote a chief magician.

The elements originally meant 'chief' ('arch-') and a practitioner of magic ('magician'); over time the compound has come to mean specifically 'a chief or supreme magician', a sense that is largely a direct combination of the original elements though usage may be figurative.