Robins took charge of the Potters last January and this season has the former Coventry City boss has steered Stoke to third place in the Championship, two points off the automatic promotion spots after 15 games.
Robins has now signed a new three-and-a-half year contract with the Championship club.
"It has been clear during his short time with the club to date that Mark is the right fit as manager of Stoke City," Potters chairman John Coates said.
"The progress we have made on the field has been extremely encouraging. Our players are responding excellently to our coaching team and the way our brilliant supporters have galvanised even further behind the club during the past year has been a pleasure to see."
