It was a second French Open crown for Djokovic after his 2016 victory and adds to his nine Australian Opens, five Wimbledon titles and three at the US Open.
The 34-year-old is the first man since Rod Laver in 1969 to win all four Slams on multiple occasions and just the third in history.
He is also the first man ever to win a Slam title by twice coming back from two sets down in same the tournament.
Djokovic had also spent more than four hours on court on Friday to knock out defending champion Rafael Nadal.
Tsitsipas survived a nervy opening service game, having to save two break points.
Djokovic, by contrast, didn't concede a point in his first three service games.
But suddenly he faced a set point in the 10th game courtesy of an ugly shank but saved it after a 26-shot rally.
Fired up by a time violation, Djokovic broke for the first time for a 6-5 lead but was unable to serve out the opener as a series of razor-sharp returns put Tsitsipas back on level terms.
In a dramatic tiebreaker, Tsitsipas saw a 4/0 and 5/2 lead disappear.
He had to save a set point before claiming the opener after 70 minutes when Djokovic fired a forehand wide.
Dropping the opening set at this year's Roland Garros was familiar territory for Djokovic.
He had to recover from two sets down to beat Lorenzo Musetti in the last 16 and lost the opener against Nadal on Friday.
Tsitsipas, 12 years the world number one's junior, broke again in the first game of the second set as the 2016 champion looked increasingly weary in the 30-degree afternoon heat.
The Greek edged ahead 5-2 and pocketed the second set with his eighth ace of the contest.
But the top seed wasn't finished, breaking in the fourth game of the third set to cut the deficit.
Tsitsipas then called the trainer to treat a back problem which also gave him the opportunity to change the clay-covered shirt he'd worn since a first set tumble.
Thirty minutes later, it was two sets apiece after Djokovic secured a double break.
As the shadows swept across Court Philippe Chatrier, Tsitsipas' mood also darkened as he slipped 3-1 down in the decider.
As the clock ticked past four hours, he fought off two more break points in the seventh game but Djokovic was not to be denied his latest slice of history taking the glory on his second championship point.