Dating from 1970, the 45-minute show was the comedy duo's first for BBC One and dates from October that year after they moved from BBC Two.
Gary Morecambe discovered seven canisters in the attic of his mother's house in Harpenden, Hertfordshire, while searching for old scripts last year.
His agent sent them off to be examined by experts who found they contained film.
One featuring part of a BBC sticker contained the lost episode, which was then colourised by the BBC.
The episode had originally been wiped from the BBC archive by the broadcaster so the tape could be reused for other programmes.
Gary Morecambe said the newly unearthed episode, which contains a sketch about a radio call-in challenge, represents "a golden era of television".
He told BBC News he was "staggered" when he received a phone call confirming the episode had been found and was salvageable.
He added: "But I didn't realise at that point how far the BBC would go to present it.
"That it would then get colourised, which is fantastic, so it's been brought bang up to date.
"And also what's really good is the quality of the show itself, you can see the embryonic Morecambe and Wise come through."
He added: "It's a bit like when they found something of Tony Hancock and Dad's Army, these are important pieces from the golden era of television so to find something that was presumed wiped, and has been sitting in an attic for 50-odd years, that is very exciting and very important."
Eric Morecambe, who died in 1984 aged 58, and Ernie Wise, who died in 1999 aged 73, are among the most popular and enduring comedy stars in British TV history.The lost episode will air on BBC Two at 7.45pm on Christmas Day.
It will be preceded at 7pm by the pair's 1971 Christmas show, featuring Andre Previn, Glenda Jackson and Dame Shirley Bassey.