The Florida endurance swimmer began her swim in Havana Saturday.
The onshore crowed joined Nyad in the water in the last few yards.
Onshore, an exhausted Nyad said her swim showed, "We should never ever give up. You are never too old to cherish your dream."
CNN said she jumped from the seawall of the Hemingway Marina into the water off Havana, and has been been swimming the Florida Strait since then. She has stopped at intervals for nourishment.
"I am about to swim my last two miles in the ocean," she said in remarks posted on her website about 11:30 EDT. "This is a lifelong dream of mine."
She praised her 35-member team, calling it a special group who were "pros and have a great heart."
"So let's get going so we can have a whopping party," she said.
Shortly before 4 a.m., her support team posted on its Twitter page: "10-mile countdown is ON!"
Nyad, a Key West native, had never come so close to Florida in her previous four attempts.
Nyad was wearing a special mask to prevent jellyfish stings to her tongue, which along with thunderstorms, factored into her failed attempt in August 2012, CNN said.
Nyad's navigator, John Bartlett, posted on her website that a favorable Gulf Stream helped her swim an average of 2.2 miles per hour.
Bartlett said currents were "smaller but less predictable" as Nyad neared Florida.
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