The 64-year-old Nyad swam up to the beach just before 2 p.m. EDT, about 53 hours after starting her journey from Havana on Saturday. As she approached, spectators waded into waist-high water and surrounded her, taking pictures and cheering her on.
"I have three messages. One is, we should never, ever give up. Two is, you're never too old to chase your dream. Three is, it looks like a solitary sport, but it is a team," she said on the beach.
"I have to say, I'm a little bit out of it right now," Nyad said. She gestured toward her swollen lips, and simply said "seawater."
Her team said she had been slurring her words while out in the water. She was placed on a stretcher on the beach and received an IV before she was taken by ambulance to a hospital. But her doctor later declared her essentially healthy and expected her to recover quickly from dehydration, swelling and sunburn.
"I just wanted to get out of the sun," she said after coming ashore on a scorching, sunny day amid calm seas.
It was Nyad's fifth attempt and what she had said would be her last try to complete the approximately 110-mile swim. She tried three times in 2011 and 2012. Her first attempt was in 1978.
"It's historic, marvelous," said Jose Miguel Diaz Escrich, the Hemingway Marina commodore who helped organize the Cuba side of Nyad's multiple attempts.
"I always thought she could do it given her internal energy, her mental and physical strength, her will of iron," said Diaz Escrich, whom Nyad has called a longtime friend.
"More than the athletic feat, she wants to send a message of peace, love, friendship and happiness ... between the people of the United States and Cuba," he added.
President Barack Obama was among a flurry of public officials and celebrities who tweeted congratulations. The president's tweet read: "Never give up on your dreams." Others who tweeted included Ryan Seacrest, who wrote "We should never ever give up ... you never are too old to chase your dreams."
Nyad later told broadcast outlet CNN her swim wasn't easy but she was determined with each stroke forward to "push Cuba back, and push Florida towards" her.
"With all that experience I have, especially in this ocean, I never knew I would suffer the way I did," she told CNN. "For 49 hours the wind just blew like heck, and it was rough."
Nyad's previous try was cut short amid boat trouble, storms, unfavourable currents and jellyfish stings that left her face puffy and swollen.
This time, she wore a full bodysuit, gloves, booties and a mask at night, when jellyfish rise to the surface. The new silicone mask caused bruises inside her mouth, making it difficult for her to speak, she told her team as she neared land.
Doctors travelling with Nyad had been worried about her slurred speech and her breathing, but didn't intervene, according to Nyad's website.
"She was incredible to watch the whole way through," said one of her doctors, Derek Covington, speaking with The Associated Press afterward.
Covington said Nyad was given IV fluids on her arrival to combat dehydration and was resting and being checked out at a medical centre as a precaution.
Although she had some swelling of the lips, tongue and the airway near the mouth, Nyad wouldn't need a long recovery, the doctor said, calling her stable and "very healthy."
Meanwhile, her website declared her team was in a mood to celebrate, with the words "Party Time."
Nyad jumped from the seawall of the Hemingway Marina into the warm waters off Havana Saturday morning to begin swimming. She paused occasionally for nourishment, but never left the water.
The support team accompanying her had equipment that generated a faint electrical field around her, designed to keep sharks at bay. A boat also dragged a line in the water to help keep her on course.
Sumaya Haddin, of Miami, had been tracking Nyad's swim before her family's weekend trip to Key West. She was surprised to see Nyad's flotilla from a parasail off Smather's Beach on Monday morning, thinking she wouldn't arrive for another day.
"You couldn't see her, you could just see the boats. It was very exciting," she said.
Haddin said Nyad still had her fighting spirit when she arrived: "Getting into the ambulance, she had her peace sign up, her fist up. She was still fired up."
Australian Susie Maroney successfully swam the Strait in 1997 with a shark cage, which besides protection from the predators, has a drafting effect that pulls a swimmer along.
In 2012, Australian Penny Palfrey swam 79 miles toward Florida without a cage before strong currents forced her to stop. This June, her countrywoman Chloe McCardel made it 11 hours and 14 miles before jellyfish stings ended her bid.
In 1978, Walter Poenisch, an Ohio baker, claimed to have made the swim using flippers and a snorkel. Critics say there was insufficient independent documentation to verify his claim.
Nyad frist garnered national attention in 1975 when she swam the 28 miles around the island of Manhattan in just under eight hours. In 1979 she swam the 102 miles from North Bimini, Bahamas, to Juno Beach, Fla., in 27.5 hours.
Nyad is also an author of three books, a motivational speaker and has been a reporter and commentator for NPR.
Associated Press writer Anne-Marie Garcia in Havana contributed to this report.