Oddie was born in Rochdale, near Manchester, and grew up in Birmingham before attending Cambridge University, where he was a member of the illustrious Footlights comedy troupe.
Before graduating, he was already writing for shows like satirical TV series That Was The Week That Was in the early 1960s.
He went on to write and appear on programmes including I'm Sorry I'll Read That Again, At Last the 1948 Show, Twice a Fortnight and Doctor in The House.
Often, he starred and wrote alongside other up-and-coming comedy names like Monty Python's John Cleese, Michael Palin and Terry Jones, and his fellow future Goodies - Tim Brooke-Taylor and Graeme Garden.
The Goodies got their own series in 1970, and the trio's slapstick comedy and madcap songs entertained millions of viewers for 12 years.
Oddie was "known as the hairy, cynical, anarchist member" of the group, the BFI said, external, and his contribution also included writing novelty songs like The Funky Gibbon and The Inbetweenies, which both reached the UK top 10.
Others paying tribute included actor and avid birdwatcher Samuel West, who wrote on X, external about the impact of watching Birding With Bill Oddie.
"Bill Oddie wore a great learning lightly, but he could never hide his enthusiasm," West said.
"His captivated, always improvised narration made that show the platonic ideal of natural history for me, and introduced a whole generation to the fascination of birds."
Naturalist and author Stephen Moss posted that Oddie "did more than anyone to popularise birding".
"Very sad news of the death of Bill Oddie: birder, comedian, musician, artist and environmental campaigner, and dear friend and colleague to me and many others," Moss wrote, external.
Oddie was a former vice president of the RSPCA, and the animal charity's current chief executive Jo Rowland said: "I know many of our wildlife rescuers were inspired into animal welfare by Bill's groundbreaking broadcasting work and incredible knowledge of British birds, which brought the wonders of nature into millions of homes across the country.
"Nature has lost one of its best friends, fiercest champions and most iconic defenders.
"Our thoughts are with his family, friends, and the countless people he inspired to spend time birdwatching, to cherish nature, and to build a kinder world for animals."
Reading FC also posted a tribute, external: "A guest of honour at many matches down the years, he became a much-loved figure at the club.
"Bill's legacy will live on through his iconic chant among Royals supporters at the SCL Stadium and around the country for many years to come."
Oddie was married to children's TV writer and artist Laura Beaumont. They have a daughter, Rosie, while Oddie and his first wife - singer and actress Jean Hart - had two daughters, Bonnie and Kate.