Kaleb Langdale, 17, survived the encounter Monday in the Caloosahatchee River west of Lake Okeechobee. Wildlife officers who caught and killed the alligator retrieved the arm, but doctors were unable to reattach it.
"We found the alligator that was responsible," Florida Fish and Wildlife Conservation Commission spokesman Jorge Pino said. "We were able to kill the alligator and dissect the alligator, remove the arm and transport the arm to the hospital to see if the doctors could reattach the limb."
The alligator was 10 or 11 feet long, Pino said.
The teen was in good condition Tuesday at Lee Memorial Hospital in Fort Myers.
His friends told Fort Myers television station WBBH that while the arm could not be reattached, Langdale was in good spirits.
The alligator went straight for Langdale as he was swimming, Matt Baker said.
"It came at him and he put his arm in the way instead of letting it get to his body. It took his arm and him under," Baker said.
Another friend said Langdale popped out of the water shortly after being bitten.
"He was waving saying, `Call the paramedics! My arm is gone!"' Gary Beck said.
The Glades County area near Lake Okeechobee where Langdale was swimming is known to have several large alligators in it, Pino said.
Alligators are more active this time of year because it's their mating season, which makes them more aggressive and inquisitive as they're looking for food and for mates. Wildlife officers warn that alligators can call just about any body of water in Florida home.
"Anything that makes any splash in the water or any little commotion in the water may attract them to that particular location," Pino said.
It's rare for wild alligators to bite humans, though, Pino said.
"We have millions of people swimming in the state's waterways and nothing happens," he said.
Since 1948, 224 people have suffered major alligator bites, including 22 fatal bites, according to June 2011 conservation commission data.
Wildlife officials were investigating what caused the alligator to bite Langdale.
"We want to understand the dynamics of the bite and understand what happened, what the alligator was doing, what the young man was doing, to see if there's anything we can learn from this," Pino said.
Last month, an airboat captain was giving a tour in southwest Florida when a 9-foot (2.75-meter) alligator bit off his left hand. The Indiana family on the boat said the captain had hung a fish over the side of the boat and had his hand at the water's surface when the alligator bit him.