The next thing I knew, I was being hurled over the handlebars and my life was literally flashing before my eyes. I really thought I was going to die."
He added that his shoulder and cheek took the brunt of the impact, and said it was lucky he was wearing a helmet.
"My bike went flying off the cliff and disappeared," he said. "We've since recovered the crumpled bicycle, completely destroyed. My cheek has been badly damaged and my knee, chin, shoulder and body severely cut.
"As I landed, once I realised I was alive, I began testing my movement. I really couldn't believe I was alive, let alone not paralysed."
Branson was taken to Miami where he underwent a series of x-rays and scans. He is hoping to pick up his training for the human endurance challenge, Virgin Strive Challenge, again next month.
He added: "My attitude has always been, if you fall flat on your face, at least you're moving forward. All you have to do is get back up and try again. At least I'm practicing what I preach - though a little too literally."
It comes after Branson was embroiled in a row with Jeremy Corbyn, after the Labour leader posted a video claiming there were no spare seats on a Virgin train he was travelling on.
