The 24-year old had spent the last five years with the Dutch giants before signing a four-year deal with Mark Hughes' side last month, having missed the majority of last season through injury.
Prior to his move, Pieters had attracted interest from a number of European clubs but he says that he has felt at home with Stoke since day one.
"I feel really good here, and the players and management have made me feel incredibly welcome, so I thank everybody for that," he told Stoke's official website.
"It's been hard work, but really enjoyable so far. The training is really good, and the players have a great friendship between them all, and I am already feeling a part of the group.
"As a boy, I dreamed of this, so to have the opportunity of playing in the Premier League for a club like Stoke really is special, and I am incredibly grateful to the club for giving me this opportunity.
"To play in a league where every team has big players is going to be a real challenge, but one that I am determined to be successful in and enjoy."
Pieters has been capped 17 times by Holland and he spoke of the influence some of his international team-mates had on his decision to move to England.
"I have a lot of friends over here, and many that I spoke to before I signed for Stoke. Tim Krul at Newcastle is my best friend, so I am looking forward to that game and have already spoken to him quite a lot already," he said.
"Then there are other lads from the national team like Robin van Persie, Ricky van Wolfswinkel and three or four at Swansea that I am really looking forward to coming up against too. It's very exciting."