Honestly, that's kind of up for debate. The Americans declared their independence in the year 1776, but it was only some signatures on a piece of paper and it had no political effect. There was a war, for real independence, which ended in 1783. As for when the colonists first arrived... British settlers started establishing themselves in the early 1600s. But before that, there had been settlers from other European nations, as well as many tribes of native peoples. It's pretty complicated.