He suffered a fatal heart attack Saturday on a cruise ship where he was giving a speech.
Frost combined serious journalism with his own celebrity status. He interviewed eight serving British prime ministers and seven US presidents.
"My heart goes out to David Frost's family," Britain's Prime Minister David Cameron said on Twitter, calling him "both a friend and a fearsome interviewer."
Frost rose to prominence in the 1960s as host of the satirical British TV programme That Was The Week That Was.
A tribute to slain US President John F Kennedy on the show was rebroadcast in the US in 1963, leading to regular appearances on television in that country.
He became an international household name following a series of interviews with disgraced former US president Richard Nixon in 1977, which later served as the basis for the 2008 film Frost/Nixon.
Frost also helped organize the 1979 Music for concert, which turned the UN General Assembly into a stage for a charity music show to raise money for the organization's children's fund.