'Tell me what your dreams are'
Nyad's home stretch followed an overnight in which she became so cold, the team didn't stop her for feeding until first light "in the hopes that swimming would keep her warm," the website said.
Every stroke she swam put her deeper into record territory. On Sunday night, she broke Penny Palfrey's record for the farthest anyone has managed on the trek without a shark cage.
In 1997, Australian Susie Maroney completed the swim from within a shark cage. She was 22 at the time.
Nyad set out from Havana at 8:59 a.m. Saturday with a crew of 35, including divers to watch for sharks.
In her first attempt to cross the Straits of Florida in 1978, rough seas left her battered, delirious and less than halfway toward her goal.
She tried again twice in 2011, but her efforts ended after an 11-hour asthma attack and jellyfish stings.
Last year, she abandoned an attempt about halfway through after severe jellyfish stings and a lightning storm put her in danger.
Nyad was a swimming sensation before these attempts. In the 1970s, she won multiple swimming marathons and was one of the first women to swim around the island of Manhattan.
She was 8 years old when she first dreamed about swimming across the Straits of Florida. At the time, Nyad was in Cuba on a trip from her home in Florida in the 1950s, before Fidel Castro led a Communist takeover in Cuba and the country's relations with the United States soured.
The Los Angeles woman had said this was going to be her final attempt.
"I decided, this one no matter what happened, I don't want that experience again -- like right now, tonight -- talking to you about the journey is worth everything. It is. But I didn't want to be here packing up again," Nyad told CNN's Gupta.
She demurred when he described her as a hero but said she hopes she can serve as some sort of inspiration.
"I think that a lot of people in our country have gotten depressed, pinned in, pinned down with living lives they don't want," Nyad said.
She continued: "I do write all the time about -- you tell me what your dreams are. What are you chasing? It's not impossible. Name it."