The family's attorney, Michael Ossi, confirmed the tragic news, telling E! News that the young man suffered a seizure at the Travolta clan's getaway at the Old Bahama Bay Hotel on Grand Bahama Island.
A police spokeswoman said Jett apparently banged his head on a bathtub Friday morning. Efforts were made to revive Jett, but he was pronounced dead at Rand Memorial Hospital, police said.
Citing privacy rules, a hospital official declined to release names, but told E! News, "We did have a young gentleman come in dead."
Meanwhile, Robert Gidel, president of Ginn Resorts, which owns Old Bahama Bay, said in a statement, "Our thoughts and prayers go out to John Travolta, Kelly Preston and their family on the tragic death of their son Jett."
"The Travolta family has become like family to us at Old Bahama Bay and we extend our deepest sympathies to them."
Jett had a history of seizures, according to Ossi. Preston had said her son suffered from Kawasaki disease, which can cause a variety of painful side effects, including seizures, and sometimes lead to heart problems.
Per Bahamian Chief Superintendent Basil Rahming, a team of officers from the Central Detective Unit were dispatched to investigate after receiving word at about 11:40 a.m. that Travolta's son had fallen ill.
Jett's body will remain at Rand Memorial pending an autopsy.
"It probably won't be until early next week that he's going to be shipped out of the country," said Glen Campbell, a mortician at the Restview Memorial Mortuary and Crematorium, which is handling the transportation of the body.
Jett, named for his dad's love of flying, was the couple's oldest child. They also have a daughter, Ella Bleu, born in 2000.
—Additional reporting by Whitney English
(Originally published Jan. 2, 2009 at 1:11 p.m. PT.)