The former Coventry City manager has signed a three-and-a-half year contract to 2028.
"At Coventry, Mark built something successful with a real identity and longevity and he left the Club in a significantly better place than he found it," said Stoke sporting director Jon Walters.
"That's exactly what we want to achieve at Stoke City, and he has all the pedigree and experience to help us do that.
"With a record like that behind him, Mark was always going to be in great demand, so we're delighted that he sees an exciting opportunity to build something special in the Potteries.
"The immediate mission is to climb as high as we can up the Championship table during the second half of this season, whilst also laying foundations for a long-term successful future for our club."