Reigning world champion An, who has held the number one ranking for the past year, beat China's sixth seed He Bingjiao 21-13, 21-16 in the women's singles final at a lively La Chapelle Arena.
The 22-year-old An is the dominant force in women's badminton and won eight titles on the sport's world tour last year.
She became South Korea's first Olympic women's singles champion since 1996.
"My golden age isn't here yet because I'm still young," she said.
"I will still have more experiences and I will be able to play even better.
He, who lost the bronze medal match at the Tokyo Olympics three years ago, progressed to the final when her Spanish opponent Carolina Marin retired from their semi-final after collapsing with a knee injury.
The Chinese player stepped onto the medal podium holding a pin badge given to her by the Spanish badminton federation.
She said she was thinking of Marin and "hoping to carry her spirit into the final".
"I feel sorry for her because she is an outstanding athlete," said He, who was visibly upset after Marin's withdrawal.
"I wanted her to watch me and I hope she recovers soon."
Marin's withdrawal meant Indonesia's Gregoria Mariska Tunjung won the bronze medal by default.
An came into the Paris Olympic after struggling with a knee injury and she said she had to "push through" it to be able to compete.
"I always try to dream big, I always try to have confidence that I can achieve that dream," she said.
"I think that's why I have been able to achieve a lot of things at such a young age."
He made An work for every point in a fast and furious first game, until the South Korean began to ease ahead towards the finish.
She closed the first game out when He smashed a return into the net.
An quickly gained the upper hand in the second game and her march towards the title began to look inevitable.
He slowed her progress with an incredible smash return midway through the game but An would not be stopped and she sealed the win on her third match point.
"I've been saving up my feelings for the last seven years for this moment," said An.
"All the agony, the frustration, this is where it all came out."
