'European-born' originates from the adjective 'European' (ultimately from Greek 'Europa', via Latin 'Europa' and Old French 'Europe'), combined with the past participle 'born' (from Old English 'boren', the past participle of 'beran', where 'beran' meant 'to carry' or 'to bear [a child]').

'European' developed from Greek 'Europa' → Latin 'Europa' → Old French 'Europe' → Middle English 'Europe' and became the adjective 'European'; 'born' evolved from Old English 'boren' (past participle of 'beran') into the modern English 'born', and the compound 'European-born' is a relatively transparent modern formation combining these elements.

Initially it meant 'born in the region called Europe' and over time has retained that core meaning as 'born in Europe' in modern usage.