The 32-year-old, ranked 25th in the world, went one better than the silver she who won four years ago in Beijing by beating Cuba's Yanet Bermoy Acosta with a yuko throw in the extra time golden score period.
After securing her win, she leapt in the air with joy, but kept her emotions in check during a later press conference.
"I'm very happy to be able to win the gold medal. By winning the gold medal I was able to glorify my nation," the very softly-spoken An said.
"By winning the gold medal I think I gave some happiness and joy to our leader Kim Jong-un."
Earlier she put out world champion and tournament favourite Misato Nakamura of Japan, a bronze medal winner in Beijing, before comfortably seeing off Italy's Rosalba Forciniti in the semi-finals.
Cuba's Bermoy Acosta, 25, had also looked impressive on her way to the final, comfortably beating Belgium's Ilse Heylen, 35, who won bronze in Athens in 2004, in the semis.
Italian police officer Forciniti, 26, won bronze thanks to the decision of the referee and two judges in a very tight battle with Luxembourg's Marie Muller, 27, who was seeking her country's first summer Olympic medal since 1952.
A clearly overjoyed Frenchwoman Priscilla Gneto, 20, beat Heylen with an ippon throw to take the other bronze in extra time.