The 24-year-old Dutch international defender joined the Potters from PSV Eindhoven on Friday for £3m.
"Of course, I've always wanted to play in the Premier League," Pieters told the club's official website.
"It's one of the hardest competitions to play in with some great players and teams and I'm really excited about it.
"I'm really looking forward to playing for this club. It's important for me that the first impression is good and I've got a great feeling about Stoke City."
Pieters has signed a four-year contract at the Britannia Stadium.