'divertible' originates from Latin (via Late Latin and French), specifically from the verb 'divertere' (Late Latin), where 'di-'/ 'dis-' meant 'apart' or 'aside' and 'vertere' meant 'to turn'. The adjective is formed with the Latin-derived suffix '-ible' meaning 'able to be'.

'divertere' changed into Old French 'diverter' (to turn aside) and Middle English forms such as 'diverten', eventually producing the verb 'divert' in modern English; the adjective 'divertible' developed by adding the suffix '-ible' to express 'able to be diverted'.

Initially it meant 'to turn aside' (the action of turning away); over time it evolved into the adjectival sense 'able to be turned aside or redirected' used in modern English.