'archonship' originates from Greek, specifically the word 'archōn', where 'arch-' meant 'ruler' and 'ōn' was an agent noun; the modern English noun is formed by combining 'archon' with the Old English/Old Norse-derived suffix '-ship' (from Old English 'scipe'/'scip') meaning 'state, condition, office'.

'archon' passed from Greek 'archōn' into Medieval and Late Latin as 'archon' and then into English; the compound 'archonship' arose by adding the English suffix '-ship' to denote 'the office or condition of an archon'.

Initially it referred specifically to the office held by ancient Greek magistrates; over time the term retained that core sense but has also been used more generally to denote the office, tenure, or authority of any archon-like official.