Conservation Foundation director David Shreeve said he died on Wednesday morning.
"David and I worked together on a variety of projects in various places since launching The Conservation Foundation in 1982," said Mr Shreeve.
"He was a larger-than-life character who became a very special friend and teacher.
"He inspired a whole generation with his wide range of interests and enthusiasm which knew no bounds.
"The Conservation Foundation was very special to him and so today is very sad for all of us."
Bellamy was a household name as a TV personality, scientist and conservationist, with his distinctive voice and delivery recognisable to millions.
He inspired Sir Lenny Henry's "grapple me grapenuts" catchphrase and was a regular presence on TV - particularly in the 1970s, 80s and 90s.
Bellamy, who was born in London but lived in County Durham, attracted criticism later in life after dismissing global warming as "poppycock".
He said he believed it cost him his TV career.
Speaking to the Independent in 2013, he said: "All of the work dried up after that.
"I was due to start another series with the BBC but that didn't go anywhere, and the other side (ITV) didn't want to know. I was shunned. They didn't want to hear the other side."
He said he stood by his opinion and that there was no hard proof it was really happening.
Radio presenter Danny Baker paid tribute to Bellamy, calling him a "truly brilliant and canny broadcaster".
Piers Morgan tweeted that he was "a brilliant naturalist, broadcaster & character".
Actor David Morrissey said: "Sad to hear the news about David Bellamy. A real character and a man who cared about nature and our environment deeply."
Former footballer Stan Collymore called him a "childhood icon".
Bellamy worked in a factory and as a plumber before meeting his wife Rosemary - with whom he had five children.
His career in the natural world began after getting a degree in botany, a subject he taught at Durham University in the 1960s.
His TV life started after his work on the Torrey Canyon oil spill, off the southwest of England, in 1967.
Bellamy's shows included Bellamy On Botany, Bellamy's Britain, Bellamy's Europe and Bellamy's Backyard Safari.
He won Bafta's Richard Dimbleby Award in 1979.