Djokovic, competing in his fifth Games, came through 7-6 (7/3), 7-6 (7/2) against Carlos Alcaraz in an enthralling final at Roland Garros to add Olympic gold to his 24 Grand Slam triumphs.
"This is probably the biggest sporting success I have ever had and the most special feeling," said the 37-year-old Serb.
"I thought carrying the flag at the opening ceremony for my country at the 2012 Olympics was the best feeling an athlete could have until today.
"Now at the age of 37 and facing a 21-year-old who is probably the best player in the world right now, winning Roland Garros and Wimbledon back-to-back, I can say that this is probably the biggest sporting success I have ever had."
Victory on Sunday allowed Djokovic to join Andre Agassi, Rafael Nadal, Steffi Graf and the watching Serena Williams as the only players to win all four Grand Slam tournaments and Olympic singles gold, completing the career Golden Slam.
Before defeating Alcaraz on Sunday, his best performance at the Olympics had been in 2008 at Beijing when he won bronze. He had also lost three semi-finals.
Now he wants to keep playing and has not ruled out trying to win back-to-back golds at Los Angeles in four years' time.
"I want to play in Los Angeles, I enjoy playing for my country in the Olympic Games, in the Davis Cup," he added.
Djokovic is the oldest singles champion since tennis returned to the Olympics in 1988 and he shattered Alcaraz's bid to add gold to the French Open and Wimbledon titles he has already pocketed this summer.
'My last chance'
An emotional Djokovic fell to his knees on Court Philippe Chatrier, where he has won three French Opens, before holding aloft the Serbian flag and clambering into the players' box to embrace his wife and children.
"We almost played three hours, the final shot was the only moment when I was sure I could win the match," said Djokovic.
His title on Sunday was the 99th of his career and first of 2024 after a difficult season in which Jannik Sinner succeeded him as Australian Open champion and eventually took his world number one spot.
Alcaraz then relieved him of the French Open before denying him the chance to equal Roger Federer's record of eight Wimbledon titles.
A knee injury suffered at the French Open required surgery and his participation in the semi-finals of the Olympics looked briefly in danger when he appeared to aggravate the problem.
"I knew that this could be my last chance of a gold medal," added Djokovic at his post-final press conference still draped in his country's flag and with his medal hanging proudly around his neck.
"I did everything I possibly could to prepare myself for this period. The injury sidetracked me a little bit. But coming into the Olympic Games I felt like a different player in terms of how I moved, how I played.
"In a way losing heavily to Alcaraz at Wimbledon probably worked in my favour as I knew I couldn't play any worse than that."
