Woods began the final round two shots behind but after a par on the 17th, he had created a two-shot lead.
Despite a bogey at 18, Woods tapped in to win his 15th major, ending an 11-year wait for a major title.
Nadal is a keen golfer in his time away from the tennis court and both have watched each other playing their respective sports.
And the Spaniard has joined a host of celebrities in congratulating the 43-year-old’s historic performance.
In a repost on Instagram of Woods holding the Masters trophy in his green jacket, Nadal wrote in the caption: “A-M-A-Z-I-N-G So happy for #Tiger You deserve it. #believe #discipline #passionforsport #inspiration.”
Nadal later said in a press conference: “It is amazing. He is probably my favourite sportsman in the world since a long time ago. I know a little bit [on] how hard he has worked to be back.
“I was very emotional yesterday.”
Yesterday, 23—time Grand Slam champion Serena Williams tweeted: “I am literally in tears watching Tiger Woods, this is Greatness like no other.
“Knowing all you have been through physically to come back and do what you just did today? Wow. Congrats a million times! I am so inspired.”
Woods’ great rival Phil Mickelson wrote: “What a great moment for the game of golf. “I’m so impressed by Tiger Woods’ incredible performance, and I’m so happy for him to capture another Green Jacket.
“Truly a special day that will go down in history. Congratulations, Tiger!”
Woods is now three behind all-time Major leader Jack Nicklaus, who said: “A big ‘well done’ from me to Tiger Woods!
“I am so happy for him and for the game of golf. This is just fantastic.
“I felt for a long time Tiger was going to win (a Major) again.
“And the next two are at Bethpage Black, where he’s won, and Pebble Beach, where he’s won.
“So, you know, he’s got me shaking in my boots, guys.”
US President Donald Trump added: “Congratulations to Tiger Woods, a truly Great Champion! Love people who are great under pressure. What a fantastic life comeback for a really great guy!”
While former US President Barack Obama said: “Congratulations, Tiger!
“To come back and win the Masters after all the highs and lows is a testament to excellence, grit, and determination.”