The legendary journalist and broadcaster's family confirmed on Sunday (1 September) that Sir David had passed away following a suspected heart attack.
A statement released to BBC News read: "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 have said the suspected heart attack occurred on Saturday evening (31 August) while he was on a cruise ship to give a speech.
Prime Minister David Cameron has said: "My heart goes out to David Frost's family. He could be - and certainly was with me - both a friend and a fearsome interviewer."
My heart goes out to David Frost's family. He could be - and certainly was with me - both a friend and a fearsome interviewer.— David Cameron (@David_Cameron) September 1, 2013
Sir David's career highlights included a series of interviews with US President Richard Nixon, which were later portrayed in the Hollywood movie Frost/Nixon, which was nominated for a string of awards including Oscars and Golden Globes.
Other shows he presented included That Was The Week That Was, The Frost Report, Breakfast With Frost, Frost Over The World and Through The Keyhole.
Tributes to Sir David have been flooding in via Twitter.
Fellow broadcaster Eamonn Holmes said: "Awful news about Sir David Frost. Was with him recently. In Broadcasting ,The Daddy of them all ! Such an influence on me and a true Gent."
Piers Morgan said: "RIP Sir David Frost > friend, hero, bon viveur, Arsenal fan and the greatest, ballsiest, most seductively charming TV interviewer ever."
Channel 4's Krishnan Guru-Murthy wrote: "Terribly sad news of David Frost's death. A huge figure in broadcasting history whose work will long be studied."