Emigration is the act of moving OUT of ones resident country with the intent to settle elsewhere. Immigration is when someone moves INTO a country from another country. Knowing which to use all depends on the order of the sentence. In your example, it first states that he moved to the United States, so the sentence should read, "He immigrated to the U.S. from the United Arab Emirates with his family as a young boy." You would use emigrate if the sentence was written as follows, "He emigrated from the United Arab Emirates to the U.S. with his family as a young boy."

In the late 1800s thousands of families left Sweden, travelled to Minnesota in the United States, and made new homes in Minnesota. They emigrated from Sweden. They immigrated to Minnesota. From the point of view of Sweden, they were emigrants. From the point of view of Minnesota, they were immigrants.