Diana Nyad managed to stand unaided as she arrived at Smathers Beach in Key West after swimming for almost 53 hours.
The 64-year-old has become the first person to complete the swim from Cuba to Florida without using a shark cage.
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The singer had been tweeting in support of migrants when she was bombarded with abusive messages.
Ministers are reportedly considering plans in a bid to lower inward migration.
In a tweet on Saturday, the US president didn't give a reason for his absence but said he wished"everyone well and have a great evening".