But 20 more might be missing, officials said.
The four Cubans reached Stock Island, just east of Key West, and reported their vessel sank because of inclement weather, the US Customs and Border Protection's Walter Slosar said on Twitter.
The US Coast Guard started a search for 23 people and found three survivors about three kilometres south of the island chain, officials said.
The survivors were taken to a local hospital and treated for exhaustion and dehydration.
Air crews continued to search for the remaining migrants.