James and Cindy Dutton, from Ruislip in west London, took to social media after son Thomas, 19, asked for Postman Pat's Prize Postbag on VHS on his handwritten gift list.
"Thomas is autistic with severe learning disability, and finds the written word easier than speaking to express himself," they said in a statement.
"It's only been the third Christmas that he has really been aware of being able to ask for presents."
The couple, who are no longer married, said Thomas wrote the list over the weekend and it consists of entirely second-hand gifts, from a Monsters University jigsaw to more videos with Postman Pat and Fireman Sam.
Thomas's parents said he has "always been obsessed with children's characters" and that one of his favourites is Postman Pat.
"He loves watching the episodes he finds on YouTube. However, he also likes having a physical copy to line up with other ones near his bed."
They had managed to find every item on Thomas's list apart from Postman Pat's Prize Postbag, so they took to social media.
Ms Dutton's plea on Facebook was shared several times, but Mr Dutton's tweet received a huge response with more than 7,500 retweets.
"It really is a wonderful story which I'm so grateful to be part of," she said. "I have three boys who, when I told what had happened, were so pleased to hear that Thomas would be getting such a great surprise on Christmas morning."
Mr Dutton, 48, a professional flautist, and Ms Dutton, 45, a nurse, said Bournemouth is "one of Thomas's favourite places" and they will collect the VHS over the weekend.
"It will mean a huge amount for him on Christmas Day," they added. "Nothing he asks for is a high-cost item, but it's all about the value to him and his innocent child-like enjoyment of life.
"We have both been overwhelmed by the response from members of the public, with so many suggestions, advice and offers to search garages and attics on our behalf!
"I think the biggest thing that we have learned is the power of social media for good things, and the kindness of complete strangers."
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