Frost suffered a suspected heart attack Saturday night aboard the Queen Elizabeth II cruise ship, where he was scheduled to give a speech, the BBC reported.
"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," his family said in a statement released Sunday morning.
Frost's career in television began in 1963, when he was featured on the BBC program "That Was The Week That Was," The Independent reported.
He went on to host "Through the Keyhole" for 20 years and then, from 2006-2012 he hosted the weekly program "Frost Over the World" on Al Jazeera English.
"My heart goes out to David Frost's family," British Prime Minister David Cameron said on Twitter Sunday morning. "He could be -- and certainly was with me -- both a friend and a fearsome interviewer."
Frost rose to fame in the United States with his series of interviews with Nixon in 2009, which were later immortalized on stage and film by Peter Morgan in "Frost/Nixon," CNN noted.
Frost is survived by his wife Carina and three sons.