Hodgkinson, already the world number one at 22, took an early lead in the Stade de France but Kenya's Mary Moraa and Ethiopia's Tsige Duguma stubbornly stuck to her right shoulder throughout the first lap.
It was only in the final stretch of the last leg of the biggest race of Hodgkinson's career that she pulled away. Hodgkinson, from Atherton, Greater Manchester, punched the air as she flew through the finish line, posting a time of 1.56.72.
Duguma, 23, ran a personal best of 1.57.15 but it was simply not good enough against Hodgkinson, whose Paris gold adds to her three European titles and silver medals at the Olympics, world championships and the Commonwealth games. Moraa, the world champion, took bronze.
Hodgkinson's imperious run made her the first British woman to win an Olympic 800m title since Kelly Holmes in Athens 24 years ago - two years before Hodgkinson was born.
She said: "I've worked so hard over the last year and you could see how much it meant to me as I crossed the line. I can't believe I've finally done it. It means so much to me. And to do it here, where better?. The audience was absolutely incredible, it felt like a home crowd to me. So I'm super happy."
Hodgkinson added: "I trusted myself, I could feel Mary [Moraa] coming at me down the back straight. But I showed composure and I got to the line first this time.
"I had a cheeky look at the screen just to make sure but you can't do anything until you cross that line. I'm now the Olympic champion for the next four years and nobody can take that away from me."
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