The 27-year-old finished with a combined total of 283kg from the snatch and clean and jerk to take second spot in the women's +87kg final in Tokyo on Monday afternoon.
Campbell beat her clean and jerk personal best (PB) by 7kg, lifting 161kg on her third and final attempt.
She earlier lifted 122kg in the snatch discipline after three attempts.
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It's Britain's first ever Olympic medal in female weighlifting
Campbell, who comes from Snape Wood Estate, was one of three British weightlifters selected for the Games alongside Zoe Smith and Sarah Davies.
In just five years Campbell has gone from a novice to competing on the biggest stage in her sport, having already been crowned European champion.
Speaking after the medal ceremony, Campbell told the BBC: “I'm actually speechless for the first time ever. I usually have a lot to say:
But, I mean you know you're in competitive shape coming to these Games. You know you want to perform your best you want to put it out there on the stage.
"I literally said to the coaches 'what just happened'? That was literally my words because like you know that clean wasn't a perfect clean. I knew I was going to have to fight.
"I just had to breath, say to myself 'you've done this 100 times, just jerk it and I did. I'm lost for words right now.
"Thanks to everyone who believed in me, you can achieve anything you want to achieve. I picked up a barbell five years ago for the first time and now I'm an Olympic medalist.
"You know, just thankyou so much for all your support. Thankyou everyone."