Mr Jones told the ABC he wanted to be a pilot, but his epilepsy ruled that out, and he believed his condition had improved enough to enable him to skydive.
"I'd been seizure-free for four years," he said.
"I've always wanted to have the feeling of flight, so I just thought, considering I can't fly a plane due to my condition, I thought I'd give it a go.
"I remember up until the point I blacked out and then waking up underneath the parachute at about 3,000 feet.
"I think I'm fairly lucky, but the emergencies [automatic activation devices] on the chutes work nearly all the time so I think I would have been OK if the jump master hadn't actually caught me."
He said he did not expect the worldwide media attention the footage has generated.
"It's a bit overwhelming, I didn't expect anything like this," he said.
