'self-possessed' originates from English, specifically the compound of 'self' and 'possessed', where 'self' meant 'oneself' and 'possessed' derives from Latin 'possidere' (via Old French 'posséder') meaning 'to have, to hold'.

'possessed' changed from Latin 'possidere' → Old French 'posséder' → Middle English forms (e.g. 'possessen'/'possessed'), and the modern English compound 'self-possessed' was formed by combining 'self' + 'possessed' to describe someone who has control of themselves.

Initially it literally meant 'possessed of oneself' (having possession or control of one's own faculties); over time it evolved into the current sense of 'calm and self-controlled'.