The Scottish journalist and writer was best known as the host of The Food Programme, a weekly radio show he created to celebrate and investigate the culinary world. It was first broadcast in 1979.
He also worked on the BBC's Tomorrow's World programme in the 1960s.
Cooper received a Sony Radio Academy Special Award for his pioneering work in food journalism and was made an OBE in 1997. He was diagnosed with Parkinson's disease nearly 20 years ago.
Among those paying tribute yesterday was food writer Jay Rayner.
He said on Twitter: "Farewell to Derek Cooper: a superb broadcaster, but more importantly a standard bearer for a robust, questioning tradition of food journalism."