The actor, best known as part of the 1970s comic trio, died on Sunday morning and is survived by his wife Christine.
Mr Brooke-Taylor began his acting career at Cambridge University where he was president of the famed Footlights performing arts club.
It was as one of The Goodies, alongside Graeme Garden and Bill Oddie, that he found international fame, earning household name status in Australia and New Zealand and attracting millions of viewers in its heyday.
His Goodies co-star Garden said he was “terribly saddened by the loss of a dear colleague and close friend of over 50 years”.
He said in a statement: “Tim and I met at Cambridge University in the early 1960s and have enjoyed working together almost constantly from that time onwards, on radio, stage, and TV.
“He was a funny, sociable, generous man who was a delight to work with. Audiences found him not only hilarious but also adorable.
“His loss at this dreadful time is particularly hard to bear, and my thoughts are with Christine, Ben, Edward and their families.”