The 30-year-old has signed an initial two-year contract, with the potential for a third year, after leaving Liverpool at the end of the 2014/15 Premier League season.
He becomes the Potters' sixth signing of the summer and has since arrived in Singapore to meet up with his new teammates ahead of the Barclays Asia Trophy next week.
Johnson, who has also served West Ham, Chelsea and Portsmouth and been capped 54 times by England, made 200 league and cup appearances for Liverpool in a six-year spell at Anfield following an £18million move in 2009.
Chief Executive Tony Scholes said: "Glen's record speaks for itself. He has a wealth of experience having a regular at international level for more than a decade and played the finals of the World Cup and European Championships.
"There was no shortage of clubs interested in him after he left Liverpool but he very much sees his future as a Stoke City player and we are delighted he has chosen to join us."
Speaking from the Far East, manager Mark Hughes said: "Glen will be a fantastic addition to our squad. He commanded a huge transfer fee when he left Portsmouth for Liverpool but dealt with the pressure that comes with that.
"He's a talented defender who also chips in with goals - as we discovered last season when he scored the winner against us at Anfield - and having spoken to him I know how much he's looking forward to being a Stoke player."