Asher-Smith stormed ahead of the chasing pack to record a time of 10.85 in Berlin.
It is the fastest a British woman has ever run.
“I am so happy. To run a 10.8 in the championships is a big deal,” Asher-Smith said.
“I knew I had it in me but anything can happen as you can see with the upsets this morning. I am so happy right now!
“I did everything right. I was so happy to nail it in the final because i know there are so many talented people around me but you have to ignore that.
“I wanted the world leading time. It is equal so I’m kind of like, eh, it was equal but I will try again later in the season.
“I am hoping to do the same thing that I did today in Tokyo!”
She becomes the first British woman since Dorothy Hyman in 1962 to win a 100m European title.
Asher-Smith’s heroics were backed up 20 minutes later when Britain’s men claimed gold and silver in the 100m final.
Men’s 100m gold and silver
Zharnel Hughes stormed to 100m victory, with Reece Prescod following up in for a silver medal.
Hughes, who ran 9.95, said: “I am happy and the job is done. I felt a bit of cramp so I don’t think I could have gone any faster but I’m just happy.
“Reece Prescod is a fast finisher so I knew I had to stay relaxed as he would challenge me towards the end. I am happy that we came out victorious.”
Prescod finished 0.01 seconds behind Hughes and said: “I wanted some consistency and I think I have got that now. It is good to have a British one-two.
“Sprinting is in a good place right now. It’s nice to have someone pushing you. We push each other hard and we run hard. I hope it continues in future Games.”
Dina Asher-Smith reaction
BBC pundit Colin Jackson was gushing over Asher-Smith’s race.
He said: “Dina Asher-Smith nailed it this time.
“No movement in the block whatsoever, she eases away and gets into her gorgeous sprinting stride and after that she’s unstoppable.
“And there’s so much more to come from her, too.”
Asher-Smith was out of the blocks fast and led rival Dafne Schippers from the off.
Indeed, Schippers was made to settle for third place (10.99), with Germany’s Gina Luckenkemper second in 10.98.
Former British Olympics gold medalist Denise Lewis said: “Shelly-Ann Fraser-Pryce-esque. Her feet were like pistons out of the blocks. It was sensational. I didn’t think I’d see that time. That has just elevated her into another stratosphere.
“Her coach has developed this world class athlete. He has worked with this young talent and it is fantastic.”
And iconic sprint kind Michael Johnson added: “That was incredibly impressive because of the time, because of the time. 10.85 was incredible, because Dina Asher-Smith didn’t even need to run that time.
“It was impressive from start to finish. We know she can start fantastically because she’s small, but she really reminded me of Shelly-Ann Fraser-Pryce here, there’s no wasted energy, shes smooth and quick and fast and efficient in her technique. And her foot-speed by the way – incredible.”