Bellamy died on Wednesday, according to the foundation, of which he was president and co-founder.
In a statement, David Shreeve, director of the Conservation Foundation, said: "Sadly, I have to report that David Bellamy died this morning.
"David and I worked together on a variety of projects in a various places since launching The Conservation Foundation in 1982.
"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."
London-born Bellamy was a household name as TV personality, scientist and conservationist.
He inspired Sir Lenny Henry's "grapple me grapenuts" catchphrase and was a regular presence on TV.
Bellamy, who lived in County Durham, later attracted criticism for dismissing global warming.
In 2004 he described climate change as "poppycock" and later said the stance 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."
Asked by the paper if he stood by his statement, Bellamy said: "Absolutely.
"It is not happening at all, but if you get the idea that people's children will die because of CO2 they fall for it."
Comedy writer and radio presenter Danny Baker has paid tribute to Bellamy, calling him a "truly brilliant and canny broadcaster".
Referencing Henry's "grapple me grapenuts" catchphrase that Bellamy inspired, Baker added: "Thoughts with @LennyHenry at this time."
Bellamy worked in a factory and as a plumber before meeting his future wife Rosemary, to whom he was still married when he died.
The couple had five children. Bellamy studied and later taught botany at Durham University.
He achieved wider recognition following his work on the Torrey Canyon oil spill in 1967. Offers for TV work followed, launching his small screen career.
Thanks to his distinctive voice and screen presence, Bellamy quickly became a popular presenter on programmes such as Don't Ask Me.
He also fronted his own shows, including Bellamy On Botany, Bellamy's Britain, Bellamy's Europe and Bellamy's Backyard Safari.
In 1979 he won Bafta's Richard Dimbleby Award.