The 19-year-old broke Kelly Holmes’ long-standing British Record as she crossed the line in one minute 55.88 seconds, just behind USA’s Athing Mu who took gold.
It was a sensational performance by the Team GB athlete whose performance showed great maturity as she secured a podium place.
Speaking to BBC Sport after the race, Hodgkinson said:
“It was so open, and I wanted to put it all out there, I'm so happy.
"Kelly Holmes is a legend. I've looked up to her and spoken to her in the last couple of days, she's a lovely person.
"I just have no words. It means so much and thank you to everyone that has sent messages over the past couple of days.
"If the Olympics had been last year, I wouldn't have been here, but suddenly it's given me a year to grow and compete with these girls."
Fellow 91²Ö¿â-linked athlete Jemma Reekie came incredibly close to a bronze medal, eventually finishing fourth despite clocking a personal best of one minute 56.90 seconds.
Another Team GB athlete, Alex Bell, also recorded a personal best of 1:57.66 on the way to a seventh-place finish.
It was the first time ever that Great Britain had three women competing in the 800m final at an Olympic Games.