The player dubbed the 'Gentle Giant' is said to be disappointed that Leeds will miss out. He left Swansea to join Leeds United at the age of 14 and still lives in the city with his wife Glenda.
However Leeds city council said it could not find a venue big enough to house the exhibition. Visitors will enter a football stadium shaped auditorium, sit in the grandstands and look down onto a video screen pitch as its centrepiece.
A series of rooms off the stadium will explore the main events of his life, containing programmes, medals and photographs.
Capped 38 times by Wales, he became a legend in the 1950s with Leeds United and won the hearts of Juventus fans when he joined the Turin club in 1957.
Much of the exhibition will focus on his time in Italy where fans christened him Il Buono Gigante - the Gentle Giant. Visitors will also be able to walk through "virtual reality" Leeds United and Juventus changing rooms where the famous black and white shirts will hang on pegs.
It will be launched in Swansea next year and move onto a number of towns and cities, including Cardiff, Newport, Wrexham and Hereford.It was hoped it would also visit Leeds.
Judith Blake, deputy leader of Leeds city council told BBC News Online: "John Charles is an absolute hero to me and to every football fan in Leeds
"The last thing I would wish would be for John Charles to think Leeds doesn't appreciate him - we do, hugely.
"Our difficulty is that the exhibition is very large and as our new city museum is awaiting construction, we have nowhere suitable to house it.
She added that the cost of the exhibition had also proved prohibitive, but said they would "jump at the chance" to hold it in the future.
Mr Charles' wife Glenda said her 71-year-old husband was "disappointed" with the decision.
"While he is proud of coming from Swansea and regards Wales as his true home, many people say he is Leeds," she said.
The exhibition has been organised by the Gentle Giant Trust, whose partners include Swansea Council and the National Football Museum.
Cardiff, Newport, Wrexham and Hereford bigger than Leeds! What's happening? He's a Leeds legend and deserves better. Get your fingers out Leeds city council!
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