Ethiopia's Tsige Duguma claimed silver and Kenya's Mary Moraa took bronze.
The fastest in the world over the distance this year, Hodgkinson took the lead halfway through the first lap and held off an attack from Duguma to finish in one minute 56.72 seconds.
Hodgkinson had arrived in Paris on a high. She set a new personal best of 1:54.61 in London three weeks ago, a result that made her the sixth-fastest woman of all time over two laps.
"It's something that I've dreamed of so much it hasn't actually sunk in yet," Hodgkinson told reporters. "The crowd was just absolutely incredible, it felt like a home Olympics for me. It just made the moment super special and I'm super happy."
Duguma won silver in a stunning Olympic debut, with world champion Moraa taking bronze.
Hodgkinson, who wore a golden plastic crown for her post-race interviews, won silver in Tokyo when she was 19 and finished runner-up in the 2022 and 2023 world championships.
"I have worked really hard for the last year and I think you can see how much it meant to me when I crossed the line," she said.
"I trusted myself, I could feel Mary coming at me down the back straight but I showed composure."
It was also a remarkable race for 23-year-old Duguma who edged out a fading Moraa to finish in a personal best 1:57.15.
Duguma burst onto the world stage in March when she won the 800 at the world indoor championships in Glasgow.
"For me, it was silver," she said.
Moraa was on Hodgkinson's shoulder for most of the race but could not match her in the last 100 metres and was overtaken by Duguma, with Shafiqua Maloney of St Vincent and the Grenadines nipping at her heels.
The Kenyan took bronze with 1:57.42, three-tenths of a second behind, and embraced Hodgkinson warmly after the finish.
The race was missing reigning Olympic champion Athing Mu, who failed to qualify after falling in the final at the US Olympic Trials. Mu, Moraa and Hodgkinson filled the podiums at the last two world championships.
