The pair were together at Chelsea from 1995 to 1998, when Stein was impressed by Hughes's fierce determination and will to win.
Stein told The Sentinel: "I think Tony Pulis was unfortunate to lose his job and I don't think anyone should forget the unbelievable job he did. But Mark will also bring that typical Stoke City spirit to the club.
"At Chelsea he was a very quiet sort of person, often kept his own counsel, but was still really good in the dressing room.
"It seems to me he's taken those attributes into management and I think this is a good appointment.
"He had a bad time at QPR, but overall his management record is good. The most important thing is he is at a good club and he is working for a chairman and family who will support him."