To be strictly correct immigrate means to move into and emigrate means to move out of. The relevant parts of the words are the im-, from Latin in meaning into and e- from Latin e-, ex- meaning out of. They sound a lot alike and get confused in colloquial speech and they do come in pairs as RubyRed pointed out. To immigrate to one place you must have emigrated from someplace else. My father's family emigrated from Scotland in the early 20th century and immigrated to America. It's like the difference between bring and take. You take your lunch from your home and bring it to work.