The 33-year-old’s contract with Stoke was set to expire this summer and the Potters have decided not to offer the veteran a new deal.
“Abdy’s contribution to getting the club where it is today should never be under-estimated,” Pulis told the club’s official website.
“He loved playing for this football club and the supporters loved him, so in many respects it is sad to see him move on.
“But we are moving forward as a club and unfortunately there are times when you have to make tough decisions that allow you to bring in the new faces which can improve the squad, and this is obviously one of them.”