The boat was returning from a fireworks display late Wednesday night when it capsized and began sinking in Oyster Bay, WNBC-TV, New York, reported.
Nassau County Deputy Inspector Kenneth Lack said one of the victims' bodies was pulled from the water Wednesday night, while the other two were recovered from inside the yacht after an overnight search. The victims, a boy and two girls, were ages 8, 11 and 12, authorities said.
The 24 survivors were pulled out of the water quickly, most being taken aboard other boats in the area, officials said.
Police investigating the incident said the accident could have been caused by the wake of another boat or severe weather passing through Oyster Bay, WABC-TV, New York, reported.
Lack said the 34-foot yacht made an emergency call around 10 p.m. and most people were quickly taken onto other crafts.
"The first person was found shortly after the distress call came in," he said. "The two others were located in the vessel. It took some time for the Mari Bureau divers to pull them out of the vessel."