The vastly experienced goalkeeper has signed a two-year contract with the Potters after being released from the final year of his deal with Aston Villa.
It represents the second time the 39-year-old has worked with Mark Hughes having been signed by him when he was in charge of Manchester City.
Given has enjoyed a glittering playing career, which has seen him win 130 Republic of Ireland caps and figure prominently in the UEFA Champions League.
City Chief Executive Tony Scholes said: "Few players can match Shay for the longevity of his career but having finished last season as Villa's first choice goalkeeper, it's clear he still has so much to offer."
Hughes added: "I know Shay particularly well from our time together at Manchester City and I'm really looking forward to working with him again.
"He will not only be a great asset on the pitch as an outstanding goalkeeper but he's also a fantastic character to have in the dressing room and around the Club - a true professional."
Given started his career with Blackburn in the mid-1990s and spent 12 years with Newcastle, with whom he clocked up more than 350 league appearances and also had a spell as caretaker manager.
After a spell with City, he joined Aston Villa in 2011 and last season played in all of their FA Cup games as they went all the way to the final against Arsenal.