The actor, best known as part of the 1970s comic trio, died on Sunday morning and is survived by his wife Christine.
Alongside Graeme Garden and Bill Oddie, The Goodies TV show attracted millions of viewers in its heyday.
Comedian Eddie Large, playwright Terrence McNally and musician Adam Schlesinger are among the public figures to have died from the virus.
A statement from Brooke-Taylor's agent said: "It is with great sadness that we announce Tim's death early today from Covid-19.
"Joining Footlights in 1960 took him to providing a huge variety of splendid entertainment - television, radio, theatre, film, books, DVDs, CDs, quizzes, etc. - all of which he undertook with energy and a great sense of fun.
"We will remember him for so much but must just mention The Goodies and I'm Sorry I Haven't A Clue. He had, of course, many fans whom he always treated cheerfully even after long and exhausting rehearsals and recordings.
"He was an exceptional client and a pleasure to represent. We're grateful that we have so much of his work to view, read and listen to.
"In all the time with us and in all his showbiz work, he has been supported by Christine, his wife."
Brooke-Taylor began his acting career at Cambridge University where he was president of the famed Footlights performing arts club.
He toured internationally with the Footlights revue in 1964 before finding wider recognition for his work on BBC Radio with I'm Sorry, I'll Read That Again.
Brooke-Taylor moved into TV with At Last The 1948 Show, where he starred alongside John Cleese and Graham Chapman.
But 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."
He was a regular panellist on BBC Radio 4's I'm Sorry I Haven't A Clue for over 40 years, and current host Jack Dee paid tribute: "It has come as devastating news to hear that Tim has succumbed to this dreadful virus - especially when we all thought he was recovering.
"Tim was a delightful man and never anything but great company.
"It's always heartbreaking to lose a loved one, but these times have created the cruelest of circumstances for that to happen in."
Sioned Wiliam, Radio 4's commissioning editor for comedy, added: "Tim Brooke-Taylor had a long and distinguished career in comedy.
"He was charming, quick witted and a hugely skilful comic.
"He was much loved both by our listeners and by his colleagues, and he will be sorely missed by all at Radio 4."