The silent snippet is all that exists of the Fab Four miming to Paperback Writer on the BBC pop show in 1966.
The original tapes were not kept, but it was recorded by a viewer filming their TV set with an 8mm camera.
The footage was shot by a family in Liverpool and eventually fell into the hands of a collector in Mexico.
The collector contacted Kaleidoscope, a Birmingham-based organisation specialising in locating previously missing TV footage.
"I think if you're a Beatles fans, it's the holy grail," Kaleidoscope's Chris Perry told BBC entertainment correspondent Colin Paterson.
"People thought it was gone forever because videotape wasn't kept in 1966. To find it all these years later was stunning."
The band pre-recorded songs for Top of the Pops on several occasions, but only appeared live once, on 16 June 1966. The performance itself has long-been a talking point for Beatles obsessives.
In 2000, a BBC spokeswoman said: "We don't know whether or not this particular piece of Top of the Pops history has disappeared forever, but unfortunately there was a time when BBC programmes were not archived as carefully as they are today and some programmes were sadly lost."
The rediscovered clip will be screened at the BFI in London as part of the Music Believed Wiped programme on 20 April.