Jett Travolta, 16, died last Friday, reportedly after hitting his head on a bathtub while on vacation with his parents in the Bahamas.
An autopsy was conducted Monday, but the cause of his death was not immediately announced, Usmagazine.com said.
However, a source close to the family told People magazine the examination revealed his death was caused by a "seizure disorder."
Jett's remains are expected to be sent by Wednesday to Ocala, Fla., where his family has a home, Usmagazine.com said.
In addition to his parents, Jett is survived by his 8-year-old sister Ella.
"We would like to extend our deepest and most heartfelt thanks to everyone who has sent their love and condolences," a posting signed, "With love, John, Kelly and Ella," said on Travolta's official Web site Sunday.
"Jett was the most wonderful son that two parents could ever ask for and lit up the lives of everyone he encountered. We are heartbroken that our time with him was so brief. We will cherish the time we had with him for the rest of our lives. We have received many messages of condolence from around the world and we want to thank everyone for their prayers and support. It has meant so much to us. It is a beautiful reminder of the inherent goodness in the human spirit that gives us hope for a brighter future."