Stein, who scored 72 goals in 134 games for Stoke, says he was sorry to see Tony Pulis leave after 10 years and two spells at the Britannia Stadium.
He 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."