Emigrate

To leave your own country in order to live in another one. It focuses on the leaving side of the move.

From Latin 'emigrare' meaning 'to move away,' from 'e-' (out) + 'migrare' (to move, migrate). English developed 'emigrate' (to leave) and 'immigrate' (to enter) as paired opposites. The difference depends on the direction you’re thinking from.