"自本国移居他国" can be translated into English as "emigrate from one's own country to another country" or more concisely as "emigrate to another country" (with the implication of leaving one's native country understood).
In a more formal or context-specific expression, you might also say:
"Migrate from one's home country to another country"
"Relocate from one's native land to a foreign country"
However, the most straightforward and commonly used term in this context is "emigrate," which specifically refers to leaving one's own country to settle permanently in another. So, "emigrate to another country" is a concise and accurate translation.