The world No 1 becomes the first man since Rod Laver in 1969 to hold all four trophies at the same time after a 3-6 6-1 6-2 6-4 victory in his fourth final at Roland Garros.
To achieve something even Roger Federer and Rafael Nadal fell short of in the same era is truly remarkable and, by winning his 12th slam title, Djokovic is only five short of Federer’s all-time record.
For Murray, it was an all-too familiar feeling as high hopes gave way to helplessness in the face of Djokovic’s brilliance, with five of his final defeats coming against the man he first faced as an 11-year-old.
The Scot, the first British man in 79 years to reach the final here, fought for all he was worth in the fourth set but ultimately he had no answer.
Djokovic lay flat on his back in the clay as he soaked in his achievement.
“It’s a very special moment,” he said. “Perhaps the biggest of my career.”
Murray apologised for not speaking French before thanking his team and the crowd.
He added: “Finally to Novak, this is his day today. What he’s achieved the last 12 months is phenomenal, winning all four of the grand slams in one year is an amazing achievement and this is something that is so rare in tennis. It’s going to take a long time for it to happen again. Everyone here is extremely lucky to see it.
“Me personally, being on the opposite side, it sucks to lose the match but I’m proud to be part of today.”
Meanwhile, Billie Jean King heralded Garbine Muguruza’s French Open victory as a changing of the guard in women’s tennis. The Spaniard produced a stunning display of power tennis to defeat defending champion Serena Williams 7-5 6-4 before collecting the trophy from King.
At 22, Muguruza joins two-time Wimbledon champion Petra Kvitova as the only grand slam winners born in the 1990s.
Muguruza announced her talent to the world two years ago by handing Williams her heaviest ever slam loss in the second round of the French Open and then lost to the American in her first final at Wimbledon last summer.
King, a 12-time grand slam singles champion, said: “The changing of the guard is starting.
“She’s the one everyone’s been talking about, for two years anyway. The kid’s got such power and she wants it. Her backhand’s just phenomenal, and her forehand too.
“The best players in the world hit down the line off a cross-court (shot) better than the others, and what does she do exceptionally well?
“She hits down the line off a cross court. It’s harder to change direction, it takes more skill, so you always look for that.You look for the movement. She’s very good at moving in with small steps. “Twenty-two is a perfect age. I won my first Wimbledon at 22. She’ll have a chance now to keep that up instead of winning big when you’re 17 and you can’t handle anything.
“You can just tell this is very good timing for what she’s going to handle off the court as well because now there’s pressures off the court that she’s never had.”
Williams’ victory over Muguruza at Wimbledon took her to within one of equalling Steffi Graf’s Open-era record of 22 slam singles titles.
And that is where she still stands after failing to get across the line in three successive tournaments.
At the US Open, when she was also going for the calendar Grand Slam, she lost in the semi-finals to Roberta Vinci, while Angelique Kerber showed Williams was now vulnerable in finals by beating her in Australia.
Having lost just four of her first 25 slam finals, losing two in a row shows, if nothing else, that Williams’ rivals are no longer daunted by facing her on the biggest stage.
Her position at the top of the rankings is not under any immediate pressure, with Muguruza now her closest rival, but Williams turns 35 in September and cannot stay there forever.