The Seattle Mariners superstar announced the big news by posing with his new American flag on Instagram Monday morning ... saying "Mission accomplished. Next stop: Registering to vote."

The 38-year-old grew up in the Dominican Republic, and has been playing in the MLB since 2005.

U.S. citizenship is becoming a trend with the Mariners -- Cruz's teammate Felix Hernandez (from Venezuela) just got his citizenship last month and was stoked about it!

"It means a lot,” Hernandez told the Seattle Times ... "Now, I am proud to be an American. Just happy, and so proud to be an American."

BONUS -- check out Cruz's stars and stripes kicks ... talk about swaggy AND patriotic.