The Spaniard beat the world number one 6-2 3-6 6-4 6-1 in New York to win his 13th career Grand Slam and the second major title of his season.
"I am very emotional obviously," he said. "Playing against Novak is also a very special feeling.
"He is an amazing player and I am sure that he will finish his career as one of the best in the history of the sport."
Nadal had previously won the US Open on one occasion when he defeated Djokovic in the 2010 final.