The 24-year-old Newham and Essex Beagles’ athlete, who became the first British high jumper to win the European title since 1950 in Helsinki earlier this year, finished third on count back as Jamie Nieto failed to clear 2.36m.
And the Games debutant was almost lost for words after winning an Olympic medal after nearly quitting the sport.
“I got a medal, I’m over the moon,” he said.
“I’m kind of sad that it’s a bronze but I got a medal, if someone said that I would get a medal in London 2012 at any point in my whole life I would have bitten their hand off.
“I had just been wasting too much time and wasn’t really applying myself. At the end of last year I sat down with my coach and he gave me a good telling off to put it politely and said you’re wasting my time, you’re wasting your time – you’re better than this.
“It wouldn’t have been possible without my mother and my coach and so many other people on the way. There’s too many to thank I just want to thank everyone.
“It’s fantastic. I am genuinely lost for words.”
Grabarz, who won a first national title in June, shared the third step of the podium with Mutaz Essa Barshim of Qatar and Canada's Derek Drouin, who both matched the Brit’s leap of 2.29m.
Meanwhile, Great Britain’s Shara Proctor cruised into Wednesday's Olympic long jump final needing only one jump to qualify.
The 23-year-old, who broke the long-standing British record at the Olympic trials earlier this year, produced a terrific 6.83m leap in the first round to ease through.
And the Birchfield Harrier athlete was delighted to get herself into the final where a medal is her only focus.
“Now all I have to do is go out there go back home and regroup and just get ready for the finals and come out and get a medal,” she said. “That’s my hope. I really hope I get a medal.
“Man, this crowd is lovely, I love it. This is what I like, they started to clap and they got right in there with me and they helped me jump the 6.83m.
“There is a seven metre jump in me."