Frost was on the cruise ship Queen Elizabeth, when he had a suspected heart attack, his relatives told the BBC.
He was 74-years-old.
The ship left Britain Saturday and was on its way to the Mediterranean, according to media reports.
The broadcasting legend was set to give a speech during the cruise when he was found dead.
A statement from his relatives said, “His family are devastated and ask for privacy at this difficult time. A family funeral will be held in the near future and details of a memorial service will be announced in due course.”
The Oscar-nominated 2008 film “Frost/Nixon” was based on Frost’s interviews with Nixon.
The film was directed by Ron Howard, and won a string of awards.
It starred Michael Sheen and Frank Langella.
In a 2009 interview about the film, Frost told CNN his conversations with Nixon were challenging.
“It was amazing to discover how … hopeless he was at small talk,” Frost said.