"I just thought I was gonna die," Parker Roll told "Good Morning America" in an interview that aired Monday.
Parker said he and his family were on vacation and had traveled with a boat crew to a secluded beach where they went swimming -- eventually coming face to face with the shark.
According to the Royal Bahamas Police Force, the incident occurred Tuesday, June 23, in Staniel Cay, a small, sandy island in the Exuma Cays.
Parker's 16-year-old brother Jack Roll said he was the one who first spotted the shark.
"I see this, what looks like a rock," Jack recalled. "I was like, 'Oh. It's a rock.' And then I see it comes closer to me. I was like, 'Oh, it's a nurse shark -- oh, it's a really big nurse shark.'"
Although the 16-year-old thought he saw a nurse shark, which tend to be docile, the brothers said they now believe it was actually a reef shark, about 8 to 10 feet long.
Shortly after spotting the animal, Jack said he heard "an ear-piercing scream" and saw the shark had latched onto Parker's leg.
Recounting the moment, Parker said he "didn't really feel [the bite] at first, because there's just so much adrenaline."
"I remember looking down, and I just see this head, and this head's well over a foot wide," Parker recalled.
Jack said he quickly jumped into action after seeing the shark bite his brother.
"I immediately took off my swimsuit, because I was like, 'Oh, we have to stop that bleeding,'" he said, adding that he managed to wrap the suit around Parker's leg before carrying him to the beach.
The boys' other brother, Adam Roll, said he alerted boat crew members.
"I immediately ran up the hill, and I started screaming to get a first aid kit," Adam recalled.
The boys said the crew then helped carry Parker back to the boat and transported the boys back to shore, about 60 miles away.
Parker recalled being in agonizing pain from the bite, saying it "felt like a knife was stabbed into my calf and then twisted, and then someone was laying on top of it."
"I've never felt pain like that, because there's lots of salt water and huge winds, and there's tons of teeth marks," Parker said.
Once on shore, Parker was transferred to an ambulance and taken to a local hospital, where he underwent surgery and received multiple stitches.
Parker said his toe was injured but his leg was intact.
"I definitely consider myself very lucky, as that shark could've easily taken my leg off," Parker said.
According to Parker's parents, doctors said they expect and are optimistic that Parker will be able to make a full recovery.
"The whole boat was praying on that ride back, because it was very, very uncertain how it was going to turn out," dad Matt Roll said.
"Very, very grateful and blessed," mom Katie Roll added.
Parker said he still experiences a lot of pain but can now walk short distances slowly. He said he is also looking forward to riding his dirt bike again and credits his older brother Jack for saving his life.
"I definitely consider him as my hero, as he stopped the bleeding and saved my life," Parker said.