The 25-year-old finished 50 points ahead of Austria’s Ivona Dadic and 113 in front of Cuba’s Yorgelis Rodriguez to take victory with 4750 points.
It ended a series of heptathlon disappointments after she finished fifth at last year’s World Championships in London, sixth at the Rio Olympics and 28th at the World Championships in 2015.
Johnson-Thompson is also due to compete in the Commonwealth Games next month and the European Championships in Berlin in August and is eager for more glory.
She said: “I said to myself I wanted two golds and one other medal but I would love three golds. If I can that would be great.
“That is what I am hoping. I am so happy. I have a busy year and this gives me confidence and belief going to the Commonwealth Games that I can compete at a certain level and come away with a medal and not screw it up.
“It means the world. It is something I have been trying to do since 2012 when I stepped into the international scene. I was disappointed last year I wasn’t able to do it outdoors.
“After the last couple of years I have had there was no pressure on me because I have not done too well. I am just happy that I can kick start this year as a gold medallist.”
She had not claimed a major medal since winning pentathlon gold at the European Indoor Championships in 2015.
Johnson-Thompson’s triumph was also Great Britain’s first World Indoor gold since 2014 when Richard Kilty took the 60m title.
Johnson-Thompson went in as favourite with the top three from last year’s heptathlon at the World Championships – Nafissatou Thiam, Carolin Schafer and Anouk Vetter – absent.
She played down her chances before the Championships but finally made her global breakthrough in a weakened field.
A lifetime best of 12.68m in the shot put kept the Great Britain star in firm contention, despite failing to seriously impose herself in the morning session.
She only cleared 1.91m in the high jump, well below her personal best of 1.98m, and failed three times at 1.94m.
Johnson-Thompson also posted an unspectacular 7.36s in the 60m hurdles, even if it did equal a season’s best as she came fifth in the heats.
She was 33 points ahead going into the final event, the 800m, but did finally dominate an event, winning in two minutes 16.63 seconds.
Earlier, Asha Philip missed out on the women’s 60m final but Elliot Giles reached the 800m final and Laura Muir, fresh from a 3,000m bronze on Thursday, eased into Saturday’s 1500m final.
Team-mate Eilish McColgan failed to join her after coming sixth in the second heat.
Muir said: “That was good, I obviously wanted to get that top two spot and that was a tough heat with Genzebe Dibaba in it but I got the job done so I’m really happy with it.
“Today I’ve been eating, seeing my physio and just relaxing as much as possible. I had the little mint chocolate from my hotel room last night and that was my ‘little treat’ but no I did the same as always.”
Sir Mo Farah is increasingly confident he can reach Tokyo 2020 as he prepares to launch his marathon career.
The four-time Olympic champion has been training in Ethiopia but will race in the Vitality Big Half in London on Sunday.
Farah is yet to make a decision over whether he will run the marathon for Team GB in Japan as he gets to grips with the new career on the road.
But, ahead of the ‘soft launch’ of his marathon running on the new 13.1 mile course, he continued to refuse to rule out a return to the Olympics having quit the track last year.
“If you’re not mixing with the guys and being close to winning medals, it would be hard to just turn up and make up the numbers,” he said. “I’m definitely more confident. But I ran 2:08 hours in 2014 and the aim is to improve on that. We’ll see how it goes. London (Marathon in April) is a big one. It’s definitely more realistic. But over the next couple of years the aim is to learn about the marathon and get better at it.
“On the track, I started building and coming up with tactics and ways to win. In the marathon, you have to work on your weakness and get stronger.
“Watching Birmingham (World Indoor Championships) yesterday, I do think about it. But my job is to get through the London Marathon and who knows? Maybe Tokyo 2020.”