Coleman presented some of British television's leading sporting programmes, including Grandstand and Sportsnight, and was the host of the Question of Sport quiz show for 18 years.
He was awarded an OBE (Order of the British Empire) in 1992 and retired from the BBC in 2000.
BBC director general Tony Hall said Coleman was one of Britain's most respected broadcasters.
"Generations grew up listening to his distinctive and knowledgeable commentary," he added in a statement. "Whether presenting, commentating or offering analysis, he set the standard for all today's sports broadcasters."
(Reporting by Stephen Addison, editing by Alison Williams)
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