The world number one downed old rival Andy Murray 3-6, 6-1, 6-2, 6-4 to claim a 12th career Major and join Don Budge in 1938 and Rod Laver, in 1962 and 1969, as the only players to simultaneously possess the French Open, Australian Open, US Open and Wimbledon trophies.
Djokovic, 29, also put himself halfway to the calendar Grand Slam, last achieved by Laver 47 years ago.
"It's a very special moment, the biggest of my career," said Djokovic, one of only eight men to complete the career Grand Slam and who had lost his previous three finals in Paris.
"I felt today something that I never felt before at Roland Garros, I felt the love of the crowd."
Djokovic imitated former three-time champion Gustavo Kuerten by drawing a giant heart in the Paris clay before collapsing inside it.
Playing in his 20th final at the majors and sixth in succession, the Serb superstar is the first man since Jim Courier in 1992 to win the Australian and French Opens back-to-back.
Victory also allowed Djokovic to stretch his winning record over 29-year-old Murray to 24-10 overall and 8-2 in Grand Slams.
(REOPENS DEL 68)
The Delhi lad was fighting hard but struggled to contain unforced errors and had to save breakpoints in the sixth game for his second hold.
Yuki had a chance to make a comeback as he had a breakpoint when Paire served for the set but the Indian hit his forehand wide. The plan was right but execution was not proper.
Some unusual unforced errors from Paire meant that he squandered three set points, serving double faults in two of them, but Paire finally took the set with an ace.
Paire was now feeling the heat with Yuki coming up with some penetrating strokes. Yuki was down a breakpoint in the third but saved it. Frustrated to let go the chance, Paire threw his racquet when Yuki served out the game.
The Indian did not help his cause by conceding a break in the fifth as Paire opened up a 4-2 lead by holding his serve in the sixth game.
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