Though Corliss, 35, is reported to have suffered severe leg injuries, he joked to South African newspaper The Cape Times that "I feel better than I've ever felt."
Corliss, who was profiled by "20/20? last year and in 2010, made a name for himself jumping from world landmarks such as the Eiffel Tower and the Golden Gate Bridge and says he has made more than 1,000 jumps.
"I was about 5 years old and I was watching these birds, and I remember seeing them open their wings and start to fly," Corliss told "20/20? in 2010. "And I remember going, you know what, when I get older I'm going to do that."
Corliss uses a flying squirrel-style wing-suit to travel at speeds of up to 300 mph and steer through the air during freefall. Watch Corliss explain how his suit works here.
"If you want to do something spectacular, something special, you have to be willing to take really unique risks," he told "20/2o."
Since his accident, authorities at Table Mountain National Park said that they do not issue permits for base jumps and that Corliss did not have permission to jump at the park. They said they will fine Corliss and could also press charges against him.
Watch Corliss complete one of his breathtaking stunts - leaping from a 7,000-foot cliff in Switzerland - and "20/20's" coverage below.