The colourful picture, entitled Rupert flies over the Suspension Bridge, depicts Rupert Bear looking up into the sky while admiring the flurry of hot air balloons flying past the famous Bristolian landmark.
Speaking exclusively to HELLO! Online, Tazia's mother Gylda Thomas explained how her daughter was a role model and a "light" to other people with Down Syndrome, and how Tazia had felt giving away her artwork.
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"Tazia thought it was a lovely thing to do, to give the painting away," said Gylda. "Especially as the Duke and Duchess had said it was going to be hung in the royal nursery.
"I think she was quite sad at first because it was a painting that she loved, but also thought that the baby would love it. It was such an honour.
"The nice thing is that since this has happened, so many parents of people with Down Syndrome have got in touch with me and have said they see Tazia as a wonderful role model. It's been a very, very positive thing for families with Down Syndrome children.
"I'm very proud of Tazia because of the painting, but I'm also proud that she's helping all these other families. She's a kind of light."
Tazia has been involved with a research project at Cambridge University, where she had to undergo different scans and blood tests.
"She didn't get paid for it but Tazia did it because she thought it would help people with Down Syndrome," said her mother.
The acrylic painting was first spotted by Heart and Sold, a charity which works to promote the artwork of people with Down Syndrome. The organisation then contacted St James' Palace and offered it to the royal couple as a gift to hang in the newborn's nursery.
"It is such an honour for this to happen, and I'm sure that the baby will love it," wrote Tazia on her blog. "I did three balloon paintings and this one is my favourite. I hope it will be Kate and Wills' favourite, too."
Tazia currently lives with her mother in Somerset, but was based in Bristol which is how she was inspired to depict the city's colourful Balloon Festival.
"That particular year that she did the painting, one of the balloons flying over the Suspension Bridge was of Rupert Bear," explained Gylda. "It's probably one of the most beautiful bridges in the world."
The picture took six months to complete and although it is estimated to be worth £2,000, Tazia has kindly offered the painting to Prince William and Kate for free.
The talented artist has been painting for the past 10 years and sold various pieces at local exhibitions, but her gift for Prince George will no doubt be her most famous work yet.
Tazia is making the final preparations for her three-week exhibition at Burnham-on-Sea in Somerset, which starts on 1 October. For details on how to view her work, visit her Facebook page or blog to get in touch with Gylda.