Check out this great infographic from The Census Bureau on migration:
[Source: U.S. Census Bureau]
There is a lot that is interesting here. First of all, the percentage of US population that is foreign-born is lower now than it was in the 19th century so, even though the foreign-born population is larger in numbers, because the US population has also grown larger, that percentage has varied in a different direction than the raw numbers.
What is not surprising is the shift in countries / regions of origin. The 19th century was the time of European migration while the more recent trends have shifted to Central America and Asia. That migrating population is also younger and distributed more widely across the US rather than concentrated on the coastal areas.
[As a side note: thanks to the Census for providing full embedding code for this infographic.]