The independent childrenswear and nursery retailer offers products for babies and children including clothing, footwear and nursery essentials.
It will launch on Wednesday 26 May and be located on the lower mall opposite TK Maxx. It will be the fifth location for Pud.
Ms McVeigh, who reached the semi-finals of the BBC reality show in 2016, said: “I am thrilled we are able to bring Pud back to the heart of Doncaster town centre. It’s always been a dream to establish Pud at Frenchgate, and I look forward to welcoming our customers back into store both old and new.
“We recently acquired nursery hardware retailer Precious Little One, so we can now diversify our offering further from prams and car seats to great quality and value clothing for your little ones.”
Frenchgate General Manager Karen Staniforth added: “We are really looking forward to Pud’s arrival at Frenchgate. We are always looking to add to our offering and childrenswear is always in high demand from our customers.
“The store looks fantastic and is very well stocked so parents and children alike can enjoy the Pud experience here at the centre.”