The world number one recovered from a nervous start to impose his pace on Court Philippe Chatrier and clinch his 12th grand slam crown after three previous failures in a Roland Garros final.
Djokovic is only the third man after Don Budge and Rod Laver to hold the four majors at the same time, and the eighth man to triumph at Wimbledon and the French, U.S. and Australian Opens.
“It’s a very special moment, possibly the biggest moment in my career,” the 29-year-old, who now has a 5-2 win-loss record against Murray in grand slam finals, said courtside.
Meanwhile, Garbine Muguruza won her first Grand Slam title on Saturday with a 7-5, 6-4 victory over Serena Williams in the French Open final, halting the world number one’s hopes of a record-equalling 22nd major.
Muguruza, 22, is the first Spanish women’s champion at Roland Garros since Arantxa Sanchez Vicario in 1998.
The 34-year-old Williams will now have to wait until Wimbledon for her next chance to pull level with the legendary Steffi Graf’s Open era record of 22 grand slam singles titles.