The 39-year-old, who was released by Aston Villa at the end of the season, was in talks with Championship side Middlesbrough as well.
But the chance to work with his former boss at Manchester City persuaded Given to sign at two-year deal with the Potters.
“He’s a quality manager and I think he’s shown to people in the last couple of years how good a manager he is as well. Had he been given a bit more time at Man City he could have done more stuff there as well, but I think he demands respect off everyone,” Given told Sky Sports News HQ.
“He wants to play good football and I think the results in the last couple of years at Stoke City has been fantastic – he’s done an amazing job.”
Stoke are looking to build on their ninth-place finish in the Premier League in the past couple of seasons, and Given concedes another factor in his decision to move to the Britannia Stadium was the appeal of still being involved at Premier League level.
“That was a big pull. Obviously Middlesbrough is a great club as well but I just felt the chance to stay in the Premier League was too big to turn down, and hopefully I’ll get that chance,” Given said.
“We’ve signed a few players and hopefully he’s talking about signing a couple more as well, so it’s exciting times to be a Stoke player, to be a Stoke fan.
“The last two seasons have been great and as a club you don’t want to stand still, you want to be pushing forward and if we can add a few more players and finish higher up the league and hopefully get close in one of the cup competitions. That will be good.”
Given feels he still has much to offer though, and is not sure his move to Stoke is the final chapter of his playing career.
“I don’t know. I haven’t really thought about when it’s all going to end,” Given said.
“I know it’s going to end one day, but I feel as fit as I’ve ever felt – obviously you’ve got to look after yourself away from football.
“I don’t know if it’s my last club or my last contract, it’s too early to say. I feel good at the minute.”