The veteran BBC interviewer died on Saturday night on board the Queen Elizabeth cruise ship, where he was giving a speech.
Known for incisive interviews with the leading figures of his time — and perhaps most famously disgraced president Richard Nixon, his career spanned more than 50 years.
In a statement, his family asked for privacy adding: A family funeral will be held in the near future and details of a memorial service will be announced in due course.”
British prime minister David Cameron described Frost as “an extraordinary man — with charm, wit, talent, intelligence, and warmth in equal measure” who had “made a huge impact on television and politics”.
“The Nixon interviews were among the great broadcast moments — but there were many other brilliant interviews,” he said.
“He could be — and certainly was with me — both a friend and a fearsome interviewer.”
Actor and comedian Stephen Fry said he had spoken to Frost only on Friday and he had “sounded so well” and was “excited about a house move, full of plans”.
Frost’s award-winning interview style was considered non-aggressive, affable, and effusive, but he had a talent for extracting intriguing information and revealing reactions from his subjects.
His roster of interviewees included virtually every US president and British prime minister during his career.
During his series of five interviews with Nixon in 1977, the notoriously slippery former president known as “Tricky Dicky” dramatically admitted to Frost that he had “let down the country”.
Frost’s appeal to American audiences saw him become one of the Concorde’s most assiduous users, and he claimed to have been on board the supersonic plane “somewhere between 300 and 500 times”.
Other historic moments in his career included a tense interview with Margaret Thatcher over the sinking of the Argentine warship the Belgrano during the Falklands conflict in which he suddenly introduced the word “bonkers”.
Frost was also the last person to interview Mohammad Reza Pahlavi, the last Shah of Iran.
Born on Apr 7, 1939, the son of a Methodist preacher, at Tenterden, Kent, Frost was educated at Gillingham Grammar School, Wellingborough Grammar School and Gonville and Caius College, Cambridge.
His big break came when he co-created and hosted satirical show That Was The Week That Was in the early 1960s.
Another of his early programmes, The Frost Report, effectively launched John Cleese, Ronnie Barker, and Ronnie Corbett on their subsequent careers.
In more recent times, he had hosted Breakfast with Frost on Sunday mornings (1993-2005) and panel game show Through The Keyhole (1987-2008).
He was currently working for Al Jazeera English and had recently interviewed Chilean novelist Isabel Allende and F1 driver Lewis Hamilton.
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
"Always warm, enthusiastic & brilliant; he will be hugely missed": BBC director-general Tony Hall on Sir David Frost http://t.co/cVminnP1Av— BBC News (UK) (@BBCNews) September 1, 2013
* “He was a remarkable man, I was lucky to know him. He was extraordinary and inspired a generation.
“An incredibly talented man, adept at so many things, an all rounder. He was part of the cultural opening up of the 1960s, and he broke boundaries.
“David was also an entrepreneur who helped put together the Two Ronnies, and helped the Pythons get together.
“The Nixon interview was a huge gamble, he had to mortgage his house, but one of the best political interviews of all time.”
* “I think fellow interviewers have always been awestruck by David Frost’s capacity to elicit memorable, sometimes historically significant quotes from all the movers and shakers or our time — presidents, prime ministers, A-list celebrities — but for all of us who had the pleasure of knowing him socially, it is his kindness, generosity, loyalty and humour that we will miss so much.
“His summer party was always the best party of the year. His fund of anecdotes and his constant wit was a joy. In fact, it was always his greeting: ‘a joy to meet you’ and it was always a joy to meet him.”
* “You couldn’t write the history of broadcasting today without realising the huge influence David had on it. From satire to comedy to the big political interviews, for more than 50 years he brought us the history of the world we live in today, that’s the mark of the man.
“I had lunch with him just three weeks ago to discuss a new series on his work. As a broadcaster and as a friend he was always warm, enthusiastic and brilliant. David was one of the BBC greats and he will be hugely missed.”
* “He was made for television and he made television. He absolutely grasped the medium and in some ways he himself almost felt that he really wasn’t actually alive unless he was broadcasting.”