Michael Jackson and George Harrison spent the next 90 minutes discussing singles by Foreigner, Nicolette Larson and The Blues Brothers, as well as the stories behind their own songs.
The BBC discarded the show, keeping only a short clip. But now a rare recording has been found and restored.
Excerpts will be broadcast in a special documentary this weekend.
Listeners will hear Jackson, just months before releasing Off The Wall, discuss how Motown refused to let him write his own music; while Harrison explains what it was like to work in the songwriting shadow of Lennon and McCartney.
At one point, Jackson turns to the former Beatle and says: "Let me ask you a question, did you guys always write your own stuff from the beginning?"
The guitarist replies: "Well, John and Paul wrote right from before we ever made a record."
Jackson seems taken aback, asking: "How did you manage that?"
"I don't know," drawls Harrison. "They were clever little fellows."
The atmosphere sounds relaxed and good-humoured throughout, and the two musicians take the task of reviewing the songs seriously, although at one point Harrison confesses: "To tell you the truth, I've no idea what is a hit and what isn't a hit these days."
The programme was part of a long-running Radio 1 series called Roundtable, which was presented in 1979 by David "Kid" Jensen.
"They were both lovely guys to talk to," he recalls of Jackson and Harrison.
"We knew we had a good show on our hands, just by the general vibe in the studio before the mics went live.
"It was like Juke Box Jury - people judging their peers. In the case of the Beatles and Michael Jackson, of course, it's not quite their peers but certainly [people] in the same line of business."
Although the broadcaster ranked the encounter as one of his favourite ever interviews, the BBC erased the programme and, for years, only low-quality bootleg recordings were available.
That was until Richard Latto, a producer at BBC Radio Solent, set about trying to find a complete copy.
"I put the word out on the collectors' circuit and a chap called Richard White came forward with a cassette recording of the entire broadcast," he says.
"This was fantastic news because the BBC only held a short, four-minute extract from the show, which is tiny when compared to the [full] programme, which contains some very special moments that were thought to be lost forever."
However, restoring the audio to a listenable standard was "a tremendous challenge", he explains.
"There's a clip on the internet which is barely audible and gives you an idea of the challenge we faced. We spent hours sharpening and polishing the raw sound, which was recorded in 1979 off an AM radio during the hours of darkness, so plagued by lots of hiss and distortion.
"After extensive work, we were able to get the voices of the legendary stars and Kid to cut through with fantastic clarity."
The results will be broadcast on BBC Radio Solent on Saturday, 9 February, the 40th anniversary of the original broadcast.
It will reveal why Jackson wore a pith helmet throughout the recording and how Harrison took a year off music to "go to the races".
On the tape, they review Foreigner's Blue Morning Blue Day ("It gets your attention" - Jackson) and Lenny White's cover of Lady Madonna ("I prefer the Fab Four's version" - Harrison).
The former Beatle discusses the merits of cover versions and discloses how he'd written the Beatles' classic Something with Ray Charles in mind.
"As it happened, the song ended up with over 150 cover versions," he says. "But when Ray Charles did it, I was really disappointed. It was a bit corny, the way he did it."
"You wrote Something?" exclaims Jackson. "Ohhhh, I didn't know that. I thought Lennon and McCartney did that."
"Yeah," Harrison replies. "Everybody thinks that."