Frost was known around the world for his interview with former President Richard Nixon.
The journalist reportedly suffered a heart attack Saturday aboard the Queen Elizabeth cruise ship that had just left the port of Southampton on a Mediterranean cruise.
He was due to give a speech on board.
In a statement to the BBC, Frost's family says its devastated and is asking for "privacy at this difficult time."
Frost was 74 years old.
The Associated Press contributed to this report.