The 26-year-old has agreed a four-year contract.
Ince previously played under Potters boss Gary Rowett at Derby, before the son of former England star Paul joined Huddersfield in 2017.
"I've had the fortune to work with Tom before and he's a terrifically talented player," Rowett told Stoke's website.
"He's very strong technically and can play anywhere across the front three, but he's particularly good from the right-hand side. His record in the Championship speaks for itself."