The programmes, presumed lost, were recorded by Everett for early commercial station, Radio Victory.
They feature his trademark homemade sound effects and jingles.
Former presenter Andy Ferris who discovered the reels said they showed Everett was "relentless in his pursuit of entertainment".
They include his creations Sing-along-with-the-Beatles, The Backward Contest and sci-fi hero Captain Kremmen.
Mr Ferris recently rediscovered the programmes in a collection of reels he purchased from the station when it lost its licence in 1986.
"At the time Everett was a household name with a very popular television show. He sent us a tape every week of one of his put-together programmes - it was great," Mr Ferris said.
"It was Kenny being funny and taking the mick and playing the music he liked at the time - he'd be very amusing and dropping in lots of sound effects."
Everett's wife at the time, Lee Everett Alkin, remembers him recording shows at their home in Cowfield, Sussex, using multi-track recorders to achieve what were ground-breaking effects for the time.
"I'd be having tea with someone and all of sudden you'd hear all these sound effects - horrendous bloodcurdling screams - from down the corridor. So in the end we sound-proofed him!"
The Victory programmes - along with remastered versions of earlier BBC Radio Solent programmes - are due to feature in a BBC documentary about Everett's life.
Producer Richard Latto, said: "It's remarkable how fresh the shows sound after all these years.
"The techniques Kenny used 45 years ago are still staggeringly impressive, but that's why he's hailed a genius by so many in the industry."
The tapes sold for Â£720 at Dominic Winter Auctioneers in Cirencester, Gloucestershire.
Kenny Everett
Rare recordings of eccentric pioneering radio DJ Kenny Everett broadcast on local radio in Portsmouth in the 1970s have been unearthed.