Alcaraz defeated Casper Ruud in four sets 7-6, 6-4, 7-6(1), 6-3 to take home the US Open for the first major tournament of his career.
Alcaraz 19, who is 19 years old, will also become the number. #1 number one ranking in the world.
Nadal who has won record-breaking 22 majors, expressed his gratitude to his fellow Spaniard on his success in the event.
"Congratulations Carlos Alcaraz on the first time you have won a Grand Slam and for number 1.
This is the end of your great season. And I'm sure will be numerous other great seasons!" Nadal wrote (according to an Google translation).
In this same tweet, Nadal also congratulated Ruud on his performance.
The 23-year-old Ruud will be the world's No. second athlete in the world after the US Open