The programme was tracked down by FIF, a charitable trust run by film collectors, cinema lovers, and vintage television enthusiasts.
Smith, who is professor of cinema and television history at De Montfort University in Leicester, and chair of trustees at FIF, said the episode was “fast-paced” and “witty” with many of the duo’s “trademarks”.
Gary Morecambe, Eric’s son, described the discovery as “wonderful” and said he thought there was not “anything out there left to find”.
“I’m so thrilled and surprised by the discovery of a Morecambe and Wise show that hasn’t been seen since 1968,” he said.
“Hats off to Professor Justin Smith and his team, whose dedication and hard work brought this gem back to us.
“I’m very excited about seeing it for the first time since I was twelve years of age.”
The episode will air on BBC Four and BBC iPlayer.