The eighth seed, booed by the crowd when he played French opponents this year, handed Serbian Djokovic his third defeat in three Roland Garros finals to add a second major to his 2014 Australian Open title.
"I played the match of my life, it's hard to believe. Playing against Novak was one of the biggest challenges. I know how much he wanted this Roland Garros," Wawrinka said courtside.
"It was a crazy atmosphere these two weeks. I'd like to thank you."
Wawrinka used his superb one-handed backhand to devastating effect, hitting flat groundstrokes that wore down eight-times grand slam champion Djokovic, who was looking to complete a career grand slam in Paris.
He sealed victory on his second match point with his 60th winner, a flashing backhand down the line that made him the second Swiss player to prevail Porte d'Auteuil after Roger Federer in 2009.
Unbeaten on clay this season, Djokovic threatened Wawrinka on his serve early on and he converted his third break chance when the Swiss served a double fault.
The Australian Open champion wasted two set points by playing too casually, and had a break point against him, which he saved with a service winner. He had a third set point that he converted when Wawrinka's forehand sailed long.