Waddell, who had been suffering from bowel cancer since last September, became known as the voice of darts for his commentary over many years on the BBC and Sky.
In a statement, his manager Dick Allix said he "died peacefully with all his family around him late last night".
Waddell also wrote BBC children's programmes Jossy's Giants and Sloggers.
He received a nomination for best scriptwriter from the Writer's Guild of Great Britain for the latter.
The broadcaster was known for his colourful and excitable commentary style.
"There's only one word for it - 'magic darts'," was one of his famous lines and he also described the challenge of a player trying to defeat multiple world champion Phil Taylor as "like eating candy floss in a wind tunnel".