The Swiss, whose only previous major title came following victory over Rafael Nadal at the Australian Open in 2014, dropped the first set against his formidable opponent but showed tremendous poise and resilience to hit back and win the match 4-6, 6-4, 6-3, 6-4.
Making his third overall appearance in the final at Roland Garros, Djokovic looked on course for a victory that would place him in very fine company after finally breaking in the seventh game.
Momentum shifted sharply on Court Philippe Chatrier, however, with the Serb losing his own serve at the pivotal moment trailing 4-5 in the second and hurling his racket to the red clay in frustration.
With his confidence growing quickly, Wawrinka broke at 3-2 in the third and never looked like giving Djokovic the chance to recover the set.
The 30-year-old then saved three break points at 4-4 in the fourth before taking another game against the head and holding his nerve to serve out for the Championship.
"I want to say thank you to the crowd. It was an incredible atmosphere on court and I felt emotion like I never have before," Wawrinka, who jumps from ninth to fourth in the rankings to leave him one place behind Britain's Andy Murray, said after his win.
"I would also like to thank Magnus Norman my coach you played in the final twice without winning but this victory is yours as well as mine."
Djokovic was understandably disappointed to have once again failed to capture the only grand slam singles title that still eludes him, but he kept his composure to pay tribute to Wawrinka and issue a statement of intent ahead of next year's event.
He said: "I want to say congratulations to Stan and it is not very easy for me to speak now, 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.
"I want to say thank you to my team, my wife and the French public. I will be back next year to try again to win the title."