The 19-year-old penned a four-and-a-half year deal at the Britannia Stadium after the Potters agreed a £3.3m fee with Birmingham City, which could rise to £3.5m.
The England international has returned to St Andrew’s on loan for the remainder of the season, and Pulis hailed the capture of Butland.
“This is a fantastic signing for the club because Jack is the best young ‘keeper in the country with an outstanding future ahead of him in the game and we are delighted to bring him here,” Pulis told Stoke’s website.
“It is important that we build for the future and this adds to the strong nucleus of young players which we have within the squad. Both this signing and the arrival of Brek Shea are significant long term investments.”
Asmir Begović is currently first-choice at the Britannia Stadium, while Dane Thomas Sorenson is acting as back-up for the Serbia international.
Butland, who made his England debut against Italy, says that he is relishing a fresh challenge in his young career at the Potters.
“I have come here to a great club, and I am looking forward to the challenge of playing in front of a great fan base,” said Butland.
“The move here ticked all of the right boxes for me, so it was quite an easy decision for me to make to be honest.
“The staff are absolutely fantastic here, and I am convinced that I will continue to develop my game here.”