Wawrinka withstood a fightback from the world number one, who was struggling with a back problem, to come through 6-3 6-2 3-6 6-3.
The 28-year-old becomes only the second Swiss man to win a Grand Slam singles title after 17-time champion Roger Federer.
And he is the first man outside the 'big four' of Nadal, Federer, Novak Djokovic and Andy Murray to win a Grand Slam since Juan Martin Del Potro at the 2009 US Open.
Fortunes fluctuated wildly over the course of two hours and 21 minutes as Wawrinka opened in scintillating form before a tearful Nadal appeared close to quitting at two sets down, only to stage a remarkable recovery in the third.
The Spaniard, 27, showed great spirit to hit back once again from a break down in the fourth, but a forehand winner gave Wawrinka the decisive break at 5-3 and he served out the biggest win of his life with a love game.
"I still think that I'm dreaming," said Wawrinka. "It's a strange feeling. I saw so many finals. I always try to watch the finals of Grand Slams because that's where the best players are playing.
"Before today, for me it wasn't a dream. I never expected to play a final. I never expected to win a Grand Slam. And right now I just did it."
Nadal, who revealed he felt the back problem in the warm-up, said: "It is a tournament that I really had some troubles physically in my career and is something that is painful for me.
"But that's part of life. That's part of sport. It's not the end of the world. Is just another tough moment."
"The last thing that I wanted to do was retire. No, I hate to do that, especially in a final.
"It's not the moment to talk about that. It's the moment to congratulate Stan. He's playing unbelievable. He really deserved to win that title."
Wawrinka had never won a set, let alone a match, in 12 previous attempts against Nadal, and was making his Grand Slam final debut against a man in his 19th.
But Nadal's travails in the second half of the match should not overshadow what was a magnificent performance from Wawrinka for much of the contest.
He coped brilliantly with the Spaniard's fizzing forehand in the early stages, using his backhand to return the fire, and 12 winners almost helped him to a 5-1 lead.
Some nerves were finally revealed when he tried to close out a set against Nadal for the first time, failing to make a first serve as he fell 0-40 down, but the 2009 champion could not get a return in play as Wawrinka hit back to seal it with an ace.
Three sweeping forehands helped the Swiss break at the start of the second on a run of 12 straight points, and it was when serving at 2-0 down that Nadal first appeared to feel the problem with his back.
After leaving the court for treatment, to the annoyance of Wawrinka and boos from some sections of the crowd, Nadal returned unable to serve at anything like full speed, and at one stage was close to tears.
Another visit from the physio followed after game five, and when Wawrinka took the second set almost unopposed, the 13-time Grand Slam champion appeared close to calling it quits on a long walk back to his chair.
What followed was remarkable, with Nadal staging the unlikeliest of fightbacks - possibly as the pain killers kicked in - while Wawrinka completely lost his rhythm with victory apparently his for the taking.
The Swiss made 19 unforced errors and, despite still not moving freely, Nadal managed to increase his service speed just enough to keep the misfiring Wawrinka at bay and clinch the third set.
It now appeared to be a test of Wawrinka's nerve as much as Nadal's fitness, because the Spaniard was clearly not about about to give up, and he clung on magnificently.
Two break points were saved at the start of the fourth, and a break recovered at 4-2 down, but Wawrinka made the decisive move with a brilliant forehand into the corner to break for 5-3 and raced through the final game.
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