"My heart goes out to David Frost's family. He could be — and certainly was with me — both a friend and a fearsome interviewer," wrote the UK Prime Minister on his Twitter page.
Sir David was most remembered for his revealing interviews with US President Richard Nixon in 1997, when the television personality skilfully coaxed the truth out of the leading politician after 29 hours of filming.
The US President admitted to his faults, revealing that he had "let down the country". At the time, Sir David had explained his persistence saying that Richard was "the most interesting person in the world."
The broadcaster also interviewed the past seven British prime ministers and seven American presidents.
"He had an extraordinary ability to draw out the interviewee, knew exactly where the real story lay and how to get at it, and was also a thoroughly kind and good natured man," said former UK Prime Minister Tony Blair.
"Being interviewed by him was always a pleasure but also you knew that there would be multiple stories the next day arising from it," added Tony. "David was a great professional and a good friend."
The presenter's death came as a great shock to his family and friends, and his relatives have released a statement asking for privacy at this time. A private funeral and a memorial service will be held in due course, they added.
Stephen Fry took to Twitter to show his shock at the news, writing, "Oh heavens, David Frost dead? No!! I only spoke to him on Friday and he sounded so well. Excited about a house move, full of plans … how sad."
Sir David clearly left a legacy in the world of media, and was well known for presenting The Frost Report, Breakfast With Frost and satirical show That Was The Week That Was.
"RIP David Frost. Met the man for the first time at the Ashes test at Lord's. What a legend," tweeted Russell Crowe on hearing the news.
"Such sad news about Sir David Frost RIP another legend has sadly left us," wrote Tamara Ecclestone.
The official statement of his death said, "Sir David Frost died of a heart attack last night aboard the Queen Elizabeth where he was giving a speech.
"His family is devastated and have asked for privacy during 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."
Sir David is survived by his wife Carina and the couple's three sons.