Both men have been praised for their courage and composure during the incident.
The men arrived to applause and a standing ovation at a press conference.
A close bond between the young surfer and his hero was soon on display, and both men also thanked the wider surfing community for their support.
Fanning said he imagined a few weeks or months would have to pass before emotional scars from the traumatic incident were healed.
Moments before the incident, he was ready and calm. The last thing on his mind was a shark.
"It went for the tail of my board, I don't know why ... it just kept coming back."
Fanning said he went into a "fight or flight" mode and started punching the shark.
He also tried to position himself away from the creature, uttering a few expletives as the animal's onslaught continued.
"At that stage I was just screaming."
He said Wilson showed great "integrity" by paddling out to help him.
"You never know what you're going to do in that situation."
Fanning stayed in fight mode, running on "instinct" a few more seconds before Wilson and surf contest organisers arrived."I had my fist cocked and ready," Fanning said.
"Luckily it didn't come."
Wilson told media he was "frozen" at first.
"Mick was looking at me. A big ol' fish popped up ... it was a lot bigger than him and I froze, I honestly froze," Wilson said.
"I was kind of freaking out ... trying to weigh up the situation."Wilson said it was terrifying when a wave obscured Fanning from his view, and he "prayed" his mate would be all right after the shark "manhandled" him.
"I was just fearing that I wasn't going to be there in time," he said.
Wilson said it was a "miracle" his friend and mentor escaped unscathed.
"He's an amazing human being and a great friend and a great role model."
Fanning said he'd heard stories from divers and surfers that punching a shark in the nose was a possible defence strategy against sharks.
"I just thought, 'Let's see what's going to happen'.
"He said it was still "an unfair fight" but he didn't want to be totally defenceless.
The surf champ said there was much research still to be done on shark behaviour.
"It's a wild animal. It's got emotions like everyone else on this planet."
Fanning said his board was 19 inches (48cm) wide and seemed "tiny" compared with the shark.
He hoped to return to the Eastern Cape surf hotspot, where he had friends and family.
"J-Bay's such a beautiful place and I'm just sad that it happened there," he said.
"I've got to go back ... you've got to face these things front-on."
He also reiterated he wanted to keep surfing.
"To turn my back on surfing ... wouldn't feel right."
He said "bottling up" one's emotions after the near-death experience would not be wise.
He said he was happy to talk and "get it all out" in the open.
"You've just got to go on with life. All that other stuff is secondary."
