The Swiss eighth seed played magnificently in a 4-6 6-4 6-3 6-4 victory at Roland Garros.
Wawrinka, 30, brought an end to Djokovic's 28-match winning streak as he claimed his second Grand Slam title.
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Djokovic had been hoping to become the eighth man to complete the set of all four major titles.
But the Serb will have to wait at least another 12 months before attempting to match the full set of major titles collected by Andre Agassi, Don Budge, Roy Emerson, Roger Federer, Rod Laver, Rafael Nadal and Fred Perry.
The 28-year-old had been a strong favourite to finally get his hands on the Coupe des Mousquetaires after beating nine-time champion Rafael Nadal and third seed Andy Murray, but he was outplayed by Wawrinka.
"It was an incredible atmosphere on court and I felt emotion like I never have before," said Wawrinka.
"I would like to thank my coach Magnus Norman. You played in the final without winning but this victory is yours as well as mine."
Djokovic was effusive in his praise for the new champion: "There are things that are more important in life than victories and that is character and respect - Stan you are a great champion with big heart."
Their last four matches in Grand Slams had gone to five sets and this was every bit as good in terms of quality, with Wawrinka hitting 60 winners as his aggression broke down the seemingly invincible Djokovic defence.
The victory makes him only the second Swiss to win at Roland Garros after Roger Federer, the man he beat in the quarter-finals.
Having lost the first set of the final following a poor service game at 3-3, Wawrinka came storming back with a barrage of winners that left Djokovic looking lost for a response.
Four break points came and went in the second set before the fifth arrived in the shape of a set point, and Wawrinka finally converted to level the match.
It was merely a sign of things to come as the eighth seed tore into the Djokovic serve in the third, and despite seeing off three break points for 1-1, there was little the top seed could do four games later.
A brilliant forehand winner was followed by an equally breathtaking backhand to earn three break points, and the first was converted as Wawrinka moved forward and hammered a short ball.
The crowd on Court Philippe Chatrier roared as the Swiss hit an outrageous winner around the net post on his way to securing the set.
Djokovic was now facing a third French Open final defeat and he dug in, taking advantage of a lull at the opposite end of the court to fashion a 3-0 lead in the fourth.
The match was now on Wawrinka's racquet, however, and he came storming back to level at 3-3 after some brilliant defence earned him the break.
Djokovic called on everything he had to stay in touch, finding two volleys - the second a lunging effort reminiscent of his coach Boris Becker - to save break points with the score level in the set.
Moments later it looked as though Djokovic would force the fifth set that had seemed inevitable as he moved 0-40 up, but there was another burst of brilliance to come from Wawrinka.
A volley, a backhand and a serve got him out of trouble, and he rode the wave of five successive points into the next game as two screaming backhand passes at 4-4 gave him the chance to serve out for the title.
It was never likely to be easy and, after a possible ace was overruled by the umpire on his first match point, the Swiss had to face a break point as Djokovic clung on to his career Slam hopes.
The Serb could only send a forehand wide under pressure, and given a second opportunity to take the championship, Wawrinka steered another of those trademark backhands down the line and raised his arms in triumph.
Stan Wawrinka stunned Novak Djokovic to win his first French Open title and thwart the world number one's career Grand Slam hopes.