Cooke has been broadcasting his weekly letter since 1946, missing only three broadcasts in almost 3,000 letters.
In a statement issued by the BBC, Cooke said: "I can no longer continue my 'Letter from America'. Throughout 58 years I have had much enjoyment in doing these talks and hope that some of it has passed over to the listeners, to all of whom I now say thank you for your loyalty and goodbye."
The corporation described him as one of the greatest broadcasters ever, drawing tributes from many senior members of staff. Mark Byford, acting director-general of the BBC, said: "It was typical of his own professionalism and love of the BBC that he wanted to explain why 'Letter from America' was coming to a close."
Among Cooke's most famous letters was his account of when JFK's brother Robert Kennedy was killed in 1968.
Jenny Abramsky, director of BBC Radio and Music, said: "I can still remember listening at university to his letter when Robert Kennedy was shot. His description of the small pantry passage way in San Francisco brought home the horror of Kennedy's death in a personal human way that marked all his letters."
Cooke has written each of his letters at a typewriter in his apartment overlooking Central Park in New York. There have been 2,869 letters since March 1946, making it the world's longest-running speech radio programme. It is estimated that he is listened to by 34m people around the world.
He was born in Manchester in November 1908 and attended Cambridge, where he took first class honours in English at Jesus College. He spent two years in the US before returning home to become a film critic for the BBC.
In 1937, he returned to the US where he began his lifetime career of reporting on American life. He hosted an American programme called 'Omnibus' in 1952 and 20 years later presented a 13-hour television series called 'America: A Personal History of the United States'.
This was later turned into a bestselling book, republished in 2001, one of many that he wrote about America and Americans.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the .
_1.jpg)
.jpg)
