The easiest way to understand these terms as well as the current usage of migrate is this:
1. emigrate = go out of a country [so...emigrated from...] or [A huge number of Irish people emigrated {went out of Ireland}during the potato famine.]
2. immigrate = to come into a country [so...immigrated to...] or [After the discovery of America, many people immigrated (went into America} in search of a better life.]
3. migrate = implies a lack of permanent settlement such a seasonal labourers or animals in search of food moving from place to place [The itinerant fruit pickers migrated from Spain to Italy and onward to...] or [The wildebeest migrate every year from their winter foraging to their spring feeding grounds...]