Unlike local alligators, the species preys on humans and is thought to be responsible for up to 200 deaths a year at home in sub-Saharan Africa.
It is possible more of the beasts are at large in the state, experts say.
It is not known for certain how they reached the US. "They did not swim from Africa," said University of Florida herpetologist Kenneth Krysko.
One likely possibility was that they were brought in illegally by unlicensed collectors, who then failed to keep them secured or intentionally released them, Mr Krysko told the Associated Press news agency.
Last place on Earth without invasive species
Aliens threaten Europe's environments
What are world's deadliest animals?
The animals were found in 2009, 2011 and 2014 and were confirmed as Nile crocodiles by a recent DNA test.
The Nile species can grow to up to 6m (20ft), significantly larger than local alligators, which commonly grow up to 4m.
They are known to prey on shrimp, fish, insects, birds and mammals, including humans. They are also known to attack livestock.
Florida wildlife experts are concerned that the African species could pose a threat to the state's ecosystem if they breed in the Everglades wetlands.
The Burmese python was first sighted in the Everglades in the 1980s and there is now an established population of the snake.
"I have two words: Burmese python," wildlife biologist Joe Wasilewski said. "If you would have told me 15 years ago we would have an established population in the Everglades, I would not have believed you."
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