Cooke died at his home in New York at midnight, a spokeswoman at the BBC's press office said. No cause of death was given, but Cooke had retired earlier this month because of heart disease.
"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," Cooke said when he stepped down on the advice of his doctor.
Prime Minister Tony Blair expressed sadness at the broadcaster's death.
"I was a big fan. I thought they were extraordinary essays and they brought an enormous amount of insight and understanding to the world," Blair told the BBC, referring to Cooke's broadcasts.
"He was really one of the greatest broadcasters of all time, and we shall feel his loss very, very keenly indeed," Blair said.
Cooke's family informed BBC reporter Nick Clarke of the death, the BBC spokeswoman said. Clarke has written a biography of Cooke.
"Letter from America," which was carried on the BBC World Service and on Radio 4 in Britain, started in 1946, and was originally scheduled to run 13 weeks.
"Alistair is a national institution," said Christopher Sarson, the original executive producer of "Masterpiece Theatre," once said. "He has defined what public television was and is for so many people that it is difficult to imagine life without him."
Born Alfred Cooke in Salford in northern England in 1908, he earned an honors degree in English from Cambridge University. In 1932 he came to the United States to study at Yale University, and he journeyed across the country by car.
"That trip was an absolute eye-opener for me," he recalled. "Even then, even in the Depression, there was a tremendous energy and vitality to America. The landscape and the people were far more gripping and dramatic than anything I had ever seen.
"It truly changed me. You see, from then on my interest in the theater began to wane, and I began to take up what I felt was the real drama going on — namely, America itself."
Returning to England and, having changed his name to Alistair, Cooke joined the BBC in 1934 as a film critic. He has been the BBC commentator on American affairs since 1938.
In a speech to the Royal Television Society in New York in 1997, Cooke traced the development of his urbane, soft-spoken style to his wartime work with the BBC.
"During the end of the war, the BBC in New York invited various famous exiles, Frenchmen mostly, to come and talk to the underground in France — famous, famous, great literary men," Cooke said.
"And I had the privilege of sitting in the control room, and I thought that I will learn about broadcasting from listening to these men...
"What I learned is that they were dreadful broadcasters. They wrote essays, or lectures, or sermons and they read them aloud. And I suddenly realized there was a new profession ahead. Which is writing for talking. Putting it on the page in the syntactical break-up and normal confusion that is normal talk," he said.
Cooke also recalled some advice when he started the program.
"A wise old talks producer came to me and said, 'Cooke, a word in your ear. Could I give you a bit of advice?' I said, 'of course.' He said, 'don't get too popular ... or they'll drop you."'
Cooke published 12 books including "Alistair Cooke's America" (1973) which sold more than 800,000 copies in hard cover.
In addition to his BBC work, Cooke was London correspondent for the NBC network in 1936-37, The Manchester Guardian's United Nations correspondent from 1945 to 1948, and chief U.S. correspondent of The Guardian until 1972.
He was host of the "Omnibus" television program in the United States from 1952 to 1961, and presented "Masterpiece Theatre" on the PBS network from 1971 to 1992.
He received four Emmy awards, three George Foster Peabody awards for broadcasting, and he was made an honorary Knight Commander, Order of the British Empire. It was an honorary award because Cooke, the consummate Englishman, had become a U.S. citizen in 1941.
Cooke's "insight, wisdom and unique ability to craft words enabled millions of listeners in the UK and around the world to understand the texture of the United States and its people," said Mark Byford, acting director general of the BBC.