French was the sixth British woman to win a modern pentathlon medal since 2000.
The Rio Games were the first since the women’s event was introduced in 2000 that Britain had not won a medal but French made up for that in spectacular fashion, keeping her cool superbly in the final run-and-shoot to set a new Olympic record.
The 30-year-old from Kent began the last event in fifth – the position she finished in Rio – but surged into the lead by the end of the first lap and never looked like letting that go, hitting her targets with her laser gun impeccably, missing just two of her 22 shots.
She follows in the footsteps of Stephanie Cook, who was the first female Olympic champion in Sydney while Kate Allenby, Georgina Harland, Heather Fell and Samantha Murray have all won medals for Britain.
French said: “I’m so, so pleased, especially after Rio. It broke the chain of the medal run. I couldn’t be more pleased to have joined the rest of the British women that have done so, so well in the past.
“I can’t say I remember watching Steph but I know Steph and have met her many times. She’s been a real inspiration in that way and also Georgina Harland. All the British women have been real inspirations.
“The British women have been so, so strong and it was in the back of my head in Rio so, to have been in Rio and not got on the podium, I couldn’t be happier to be on the podium here.”
French was considered a strong medal prospect having won gold at the World Cup Final earlier this year.
She was disappointed with her fencing display on Thursday despite sitting sixth, and she dropped to eighth after the 200 metres freestyle swim on Friday, which for the first time took place in the same venue, with a temporary pool erected at one end of Tokyo Stadium.
French was then one of very few riders to go clear in the show jumping, although she did pick up six time penalties.
Modern pentathlon was devised by Baron Pierre De Coubertin, the founder of the modern Games, who selected the disciplines to simulate the challenges faced by an infantryman caught behind enemy lines.
A key element of the sport is riding an unfamiliar horse, with athletes given only 20 minutes to bond with their mount before their round.
French said: “When I first got on the horse it wasn’t the sort of horse I like riding. My riding instructor had to really get after me to ride it forward and she gave me confidence in how to ride the horse.
“I think we worked well together in the end. I really enjoyed the riding, I couldn’t have been happier with that.”
The show jumping has scuppered many a pentathlete’s hopes and so it proved again, with Ireland’s Natalya Coyle among those to drop right down the field.
Germany’s Annika Schleu, meanwhile, must have harboured strong medal chances after setting an Olympic record in the fencing. She was still well out in front after the swim but never got to grips with her horse – the misnamed Saint Boy – and left the arena in tears and with no points.
French has no great horse-whispering secrets, saying: “I give the horse a pat, just walk around, get a feel of the horse and then just have a few jumps.”
The final event, the run-and-shoot, sees athletes complete four legs of 800m and four rounds at the range, where they must hit five targets each time.
The leader goes off first, with each point adrift converted to one second, and the top five were all within 15 seconds, which quickly became academic as French pulled away for a solo victory ahead of 2012 gold medallist Laura Asadauskaite of Lithuania and Hungary’s Sarolta Kovacs.
French said: “Yesterday wasn’t such a perfect day so I’m really pleased I managed to come out fighting today and turn things around.
“I really tried to stick to my plan and stay focused. I knew if I did that I could be in contention but I tried not to think too much about getting a medal. I’m so pleased I was able to hold it together.”
She stood proudly atop the podium, and said of her gold medal: “It’s been on my mind a long time. It’s always been a dream and I can’t believe it’s come true.”
Britain also has a good chance of a first Olympic medal in the men’s competition on Saturday, with Joe Choong in first place after the fencing.