Although Djokovic came into Sunday's clash on Court Philippe Chatrier having won the last three slams, taking his overall tally to 11, success at Roland Garros had eluded him - the Serbian falling at the final hurdle in 2012, 2014 and 2015.
That agonising run looked set to continue when an error-strewn first-set performance from the world number one enabled Murray to move ahead in confident fashion.
However, Djokovic responded superbly, controlling proceedings thereafter to triumph 3-6 6-1 6-2 6-4 and become the eighth man in history - after Fred Perry, Don Budge, Rod Laver, Roy Emerson, Andre Agassi,Roger Federer and Rafael Nadal - to win all four major titles. Even more impressively, he is now the holder of each grand slam trophy.
A vastly improved player on clay over the last two years, Murray had claimed a morale-boosting win over Djokovic when the duo last met in Rome three weeks ago, having lost 12 of their last 13 meetings.
And it was the Briton - in his maiden French Open final appearance - who swiftly seized the initiative early on, despite being broken to love in the opening game.
Djokovic's forehand proved surprisingly unreliable as he slipped 4-1 down and an aggressive Murray took the lead by winning a game that was briefly interrupted by whistling from spectators, who were unhappy with an umpiring call that had gone against the top seed.
Murray had never previously lost at Roland Garros when winning the first set, but it was not long before he found himself firmly on the back foot.
Djokovic's initial struggles appeared a distant memory as he raced through the second set, holding with increasing ease and applying constant pressure when returning.
With Murray unable to halt the momentum of an opponent who frequently excelled at the net with a host of sparkling winners, the relentless Djokovic duly kicked on.
After earning a double-break in set three, he staved off a brief Murray revival - that yielded four break points - before opening up a similar advantage in the fourth.
Murray, taken to five sets in each of his first two matches at this tournament, impressively mustered the energy and resolve to break back when Djokovic served for the match at 5-2.
However, Djokovic was not to be denied as he got the job done in his next service game, albeit after spurning two championship points amid rising tension, to join an exclusive club of greats.