Nyad arrived at the beach just before 2 p.m. EDT, about 53 hours after she began her swim in Havana on Saturday.
As she approached, spectators surrounded her in the water, taking pictures and cheering her on. Once on the beach, she was put on a stretcher and received medical treatment, including an IV. Her lips were swollen.
President Barack Obama Tweeted: "Congratulations to @DianaNyad. Never give up on your dreams."
This marked Nyad's fifth try to complete the approximately 110-mile swim. She tried three times in 2011 and 2012. She had also tried in 1978.
Her last attempt was cut short amid boat trouble, storms, unfavorable currents and jellyfish stings that left her face puffy and swollen.
"I am about to swim my last 2 miles in the ocean," Nyad told her 35-member team from the water, according to her website. "This is a lifelong dream of mine and I'm very very glad to be with you."
Nyad told supporters a silicone mask she wore to protect her face from jellyfish stings caused bruises inside her mouth, making it difficult for her to talk.
Doctors traveling with Nyad were worried about her slurred speech and her breathing, but they didn't intervene, according to Nyad's website.
"I admit there's an ego rush," Nyad said before the swim began. "If I – three days from now, four days from now – am still somehow bringing the arms up and I see the shore ... I am going to have a feeling that no one yet on this planet has ever had."
Andrew Innerarity / Reuters / Landov
Team Kept Sharks AwayNyad's journey began Saturday morning when she jumped from the seawall of the Hemingway Marina into the warm waters off Havana. She stopped from time to time for nourishment.
The support team accompanying her had equipment that generated a faint electrical field around her, which was designed to keep sharks at bay. A boat also dragged a line in the water to help keep her on course.
Nyad wore a full bodysuit, gloves, booties and a mask at night, when jellyfish rise to the surface. Before the swim, she said the kit would slow her down, but she believed it would be effective.
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 abandon the attempt. 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 first came to 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.