Mr Cooper was best known as the host of The Food Programme, a weekly radio programme he founded to celebrate and investigate the culinary world and first broadcast in 1979.
His work appeared regularly in Scotland on Sunday, as well as the Guardian, the Listener and Saga Magazine.
He also worked on the BBC's Tomorrow's World programme in the 1960s.
Born on 25 May 1925, he attended Portree High School and Wadham College, Oxford. He later received an honorary D.Litt from Queen Margaret University College, Edinburgh.
He was diagnosed with Parkinson's disease in 1995.
In 2001 Mr Cooper received a Sony Radio Academy Special Award for his pioneering work in food journalism and was made an officer of the Order of the British Empire (OBE) in 1997.
The Food Programme Twitter account said Mr Cooper was "a man who reintroduced a nation to its food culture".
The @BBCFoodprog account tweeted: "Sad to announce that the founding presenter of The Food Programme, the journalist and broadcaster Derek Cooper has died."
Mr Cooper was also the first chairman and president of the Guild of Food Writers. Since 2002, the Guild has given out the Derek Cooper Award for campaigning and investigative food writing and broadcasting.
Food writer Jay Rayner, who was a recipient of the Derek Cooper award last year, said Mr Cooper was a "standard bearer" in food journalism.
Rayner said on Twitter: "Farewell to Derek Cooper: a superb broadcaster, but more importantly a standard bearer for a robust, questioning tradition of food journalism."
Broadcaster and comedian Hardeep Singh Kohli tweeted: "Derek Cooper. The comforting voice of a generation. RIP."
Mr Cooper also featured on Radio 4 programmes PM, Today, and You and Yours. He began his career at Radio Malaya in 1950 and worked at ITN before becoming a familiar voice of BBC radio and television shows.
Among his published work is The Bad Food Guide, The Beverage Report, Guide to the Whiskies of Scotland, Wine With Food, The World Of Cooking and The Little Book of Malt Whiskies.
He had a close interest in the Highlands and Islands, particularly Skye and the Outer Hebrides. His book, The Road to Mingulay, is an account of his journey across the Hebridean archipelago to Mingulay, where his grandmother Seonaid was born.
There is also a collection of the best of his writing over the last three decades under the title, Snail Eggs and Samphire.