The NY Yankees fireballer -- nicknamed the "Cuban Missle" -- defected from Cuba (by way of the Netherlands) back in 2009 ... and has made it his mission to get full citizenship.
Well, Friday it finally happened ... and the 28-year-old proudly announced it on social media.
"Today is a very important day for me and I want to share it with all of you," Chapman wrote.
"Today April 29, 2016 I've became a U.S. Citizen and I want to thanks God and this great nation for the opportunities it has offer me and my family. Very happy to say that I'm a U.S. Citizen."