Djokovic had finished runner-up three times in Paris
World number one Novak Djokovic beat Britain's Andy Murray to win his first French Open title and complete the career Grand Slam.
The Serb, 29, won 3-6 6-1 6-2 6-4 to win his 12th major title and become the first man since Rod Laver in 1969 to hold all four Grand Slams at once.
Murray had hoped to secure the third leg of his own career Slam, having already won Wimbledon and the US Open.
The Scot, 29, was Britain's first male finalist in Paris since 1937.
Second seed Murray played superbly to win the first set but could not convert a break point early in the second, and Djokovic took control to win in three hours.
He becomes only the eighth man in history to have won all four of the sport's major singles prizes - and could yet match Laver's achievement of winning all four in a calendar year.
Djokovic fell back on the clay in delight and relief after requiring two breaks of serve and four match points in a desperately tense end to the final.
Murray has now lost eight of his 10 Grand Slam finals
With three-time champion Gustavo Kuerten watching from the stands, Djokovic then emulated the Brazilian by drawing a heart in the clay with his racquet.
"It's a very special moment, the biggest of my career," said Djokovic. "I felt today something that I never felt before at Roland Garros, I felt the love of the crowd.
"I drew the heart on the court, like Guga, which he gave me permission to do. My heart will always be with you on this court."
Murray, who has now lost five Grand Slam finals to Djokovic, had looked capable of causing an upset with an aggressive display in the opening set.
However, Djokovic turned the match around early in the second set and Murray, who had played five hours' more tennis in reaching the final, could not keep pace.
"To Novak, this is his day," said Murray. "What he's achieved the last 12 months is phenomenal; winning all the Grand Slams in one year is an amazing achievement.
"It's so rare in tennis, and for me personally, it sucks to lose the match, but I'm proud to have been part of today."
Djokovic looked determined to make up for losing in three previous Paris finals when he broke the Murray serve to love with a brilliant opening game, but the nerves were soon apparent.
A beautiful lob saw Murray hit straight back in game two and, playing aggressively at every opportunity, he powered into a 4-1 lead as Djokovic misfired with his forehand.
Murray was hoping to emulate Fred Perry's French Open victory of 1936
Murray clinched the set at the third opportunity - after a generous overrule that drew boos from a crowd seemingly backing Djokovic - and some stunning defence earned the Scot a break point at the start of the second set.
Djokovic needed to turn the tide and he did so with a smash, before grabbing the lead when Murray double-faulted at break point down.
The Serb then began to dictate with his backhand, firing a winner down the line for a decisive second break as Murray's first-serve percentage slipped below the 50% mark.
Djokovic continued to press, setting up break points at 1-1 in the third set with a forehand winner and watching as Murray dropped a volley into the net with the court gaping.
The crowd chanted "Nole! Nole!" as the world number one finally regained the lead he had surrendered after the opening game of the match, and he broke again with a terrific sliding winner on his way to a two-sets-to-one lead.
With a 5-2 lead in the fourth set, and his friends and supporters preparing to celebrate in the stands, Djokovic suffered a tortuous few minutes as Murray refused to give up.
The Briton got one of the breaks back and saved two match points, before finally netting a backhand as Djokovic clinched a historic win.
Djokovic follows Rod Laver and Don Budge as holder of all four Slams at once
Pat Cash, former Wimbledon champion: "This has been the tricky one for Djokovic but he's come out and played some great tennis. He's rock solid, he knows his game so well and he's mentally focused. From where he started off in this match to where he finished, what a contrast, and it just goes to show how great a champion he is."