London-born Bellamy, who became a household name as a TV personality, scientist and conservationist, died on Wednesday, according to the foundation.
His colleague, David Shreeve, described him as a "larger-than-life character" who "inspired a whole generation".
In later life Bellamy, who lived in County Durham, attracted criticism for dismissing global warming.
In 2004 he described it as "poppycock" - a stance which he later said cost him his TV career.
Bellamy worked in a sweet factory and as a plumber before embarking on his broadcasting career.