The 22-year-old completed the £3.25 million move for Portsmouth on Monday and has signed a four-and-a-half year contract with Stoke.
“It has been an eventful time for me, one way or another, but I am delighted to be joining Stoke because it is a Club moving forward,” Begovic told the club’s official website.
“I was aware of interest from one or two clubs, but once I found out that Stoke wanted to sign me, I was convinced that it was right move for me.”
He added: “My time at Portsmouth has been great for my development, but this is an exciting new challenge for me to push on in my career.”
