Dan and Kate Suski were on a charter boat Sunday fishing when it began taking on water and sank, CNN reported.
Their older brother, David Suski, said he had spoken with his siblings and "they told me they had a fish on the line, and were fighting the fish, then heard a noise."
The boat's captain checked the engine room and saw it was filling with water, David Suski said.
It took about "3 to 5 minutes from the time they heard the noise to when they had to abandon the boat and it sank," he said.
The siblings, the boat's captain and a crew member wound up in the water with only their life jackets.
"It was intense. It was a long day, a long 29 hours," Dan Suski, a 30-year-old information technology expert from San Francisco, told WSVN-TV.
"It was completely surreal."
His sister, a 39-year-old architect from Seattle, agreed.
"It was a series of incredible challenges," she told the Miami TV station.
"We could see land off in the distance and started swimming in that direction.
"Surf was crashing into the cliffs, and we decided that we should keep swimming and found a very small sliver of beach, and we were able to get to safety that way."
A Saint Lucia resident found the Suskis on a beach later that night, CNN said. The boat captain and crew member were found later. All four were brought to a local hospital.
"They are feeling lucky to be alive -- it was quite an ordeal -- both my brother and sister were treated for dehydration and when they made it [to] shore, they drank from a stream, so they also were given antibiotics in case the water wasn't clean," David Suski said.
The Suskis spent two days at the hospital and were expected to return to the United States Sunday.