The TV star, who found fame in the 1970s as a member of comic trio The Goodies alongside Tim Brooke-Taylor and Graeme Garden, died on Saturday, he agent said.
He went on to host wildlife programs for the BBC, including Birding With Bill Oddie, Bill Oddie Goes Wild, Springwatch and Autumnwatch.
"It is with deep sadness that I announce the passing of Bill Oddie, the country's best-loved birder," a statement from his friend and agent David Foster said on Monday.
"Bill was a multi-talented celebrity – wildlife presenter, broadcaster, comedian, writer, songwriter, musician and conservationist.
"Yet it was never fame that he valued. Instead he encouraged us to respect and protect the environment.
"He taught us the wonder of it. He protested, lobbied and campaigned for it. He led the way and people of all ages and backgrounds responded to his call. And such a massive contribution to conservation will never be forgotten.
"As Bill's agent I witnessed close hand his intelligence and wit. He was my friend and it was an honour and a privilege to represent him for so many years. I will miss him terribly.
"My thoughts and love are with Bill's wife, Laura, and his daughters Bonnie, Kate and Rosie, who have asked not to be contacted at this sad time. Please respect their wishes."
A birdwatcher since his childhood in Birmingham, Oddie was a respected ornithologist and represented many nature organisations.
In addition, he wrote a number of books on birds and other wildlife topics.
His comic career began in Cambridge Footlights, when he started writing for shows including That Was The Week That Was.
He went on to write and appear on numerous programmes including I'm Sorry I'll Read That Again, which featured many of his comic songs.
He first found fame as a member of The Goodies and the trio earned household name status in Australia and New Zealand, as the television comedy show attracted millions of viewers in its heyday.
His songs led the Goodies to several major chart hits, most notably The Funky Gibbon.
He continued to work with his fellow Goodies on program including Bananaman, before turning his attention to nature shows.
Oddie spoke openly about suffering from crippling depression, and he was admitted to a psychiatric hospital in 2009 after being dropped from the BBC show Springwatch, of which he was one of the original presenters.
He was finally diagnosed with bipolar disorder, a condition where depressive periods alternate with manic activity.
Speaking in 2014, he said he still felt a lingering sadness that his days on Springwatch were cut short but supported its encouragement for people to enjoy the natural world.
"That's all to the good because I fear so many people wear earphones for their phones and music players that increasingly they miss out on everyday joys like birdsong," he said.
"My plea to people would be to 'go naked' occasionally – take off those earpieces so you hear nature and, of course, birdsong. You may not realise how precious it is until it's gone."
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