Djokovic, who has won a men’s record 24 majors and swept up every title there is in tennis, finally clinched Olympic gold at his fifth Games.
The Serb, 37, put in his best performance of the year to beat French Open and Wimbledon champion Alcaraz 7-6 (7-3) 7-6 (7-2) in front of a packed crowd in Paris.
He sealed the title with a forehand winner, then turned towards his box – arms outstretched in disbelief – before throwing his racquet to the floor after a draining match which lasted just under three hours.
After hugging Spain’s Alcaraz, Djokovic immediately burst into tears and fell to his knees in the middle of the court.
He then unfurled a Serbian flag and clambered into the stands to celebrate with his family and support team.
Djokovic is just the fifth player to win the ‘Golden Slam’ in singles – all four majors and the Olympic title – after Rafael Nadal, Serena Williams, Andre Agassi and Steffi Graf.
“Everything I felt in that moment when I won surpassed everything I thought or hoped that it would,” said Djokovic.
“Being on that court with the Serbian flag raising, singing the Serbian anthem, with the gold around my neck, I think nothing can beat that in terms of professional sport.
“It definitely stands out as the biggest sporting achievement I have had.”
Alcaraz, 21, was also in tears after the match, but will leave with a silver medal on his Olympic debut.
Italy’s Lorenzo Musetti is the singles bronze medallist, having beaten Felix Auger-Aliassime of Canada on Friday.