Marine Police Sgt. Finley Leonce told The Associated Press that the captain and first mate were rescued on Monday around noon by a private boat owner who was helping with the search.
"They were waving their arms," he said. "They were still swimming to shore."
The two men are employees of a local company called "Reel Irie", which owns the 31-foot (9-meter) boat that sank on Sunday off the north coast of St. Lucia while on a fishing trip. Also aboard the boat were Dan Suski, a 30-year-old business owner and information technology expert from San Francisco, and his sister, Kate Suski, a 39-year-old architect from Seattle.
Leonce said authorities picked up the Suskis on Monday near Dauphin Beach on the island's northeast coast. The Suskis told the AP that they swam for nearly 14 hours, reached shore, and then hiked for about three hours the next day until they found a farm worker who called police for help.
All four of the survivors, who had been wearing life jackets, were hospitalized and treated for dehydration and various injuries.
An unidentified man who answered the phone at the "Reel Irie" company on Friday declined to comment. He only said that captain Griffith Frederick and mate Tim Cooper are doing well and that they are not providing interviews.
The boat's make and model were not available. Leonce said police did not have those details.
Leonce said the local weather service had issued a small craft advisory the day the boat sank, meaning that all small boats should remain close to shore.
"The sea conditions were very deplorable," he said.
About four hours into Sunday's fishing trip, the boat began taking on water amid heavy swells.
When authorities received the captain's distress call, they dispatched a boat immediately, but it took 30 minutes to reach their location, Leonce said.
Police also dispatched a helicopter and a small plane, and about nine private boat owners helped in the search, which was called off Sunday night and resumed early Monday, he said.
"Visibility was very poor on Sunday," he said. "The weather conditions were not the best. It was raining intermittently, with sometimes very heavy showers."
A preliminary investigation shows that the boat's bilge system could not handle the amount of water coming in, Leonce said.
"It's a little too early for me to say definitively what happened," said Leonce, adding that foul play has been ruled out.