The Senegal international, who had long been linked with a switch to Stoke, will finally join the club on July 1 after his contract with Hannover expires.
Diouf, who has penned a four-year deal at the Britannia Stadium, has previously had spells with Manchester United and Blackburn Rovers, but struggled to make his mark in the English game.
"This is a chance for me to prove myself in the Premier League," he told Stoke's official website.
"When I was at Manchester United, I didn't get the chance to play many games and went on loan to Blackburn.
"It didn't go as well as I wanted and I opted for a new experience in Germany.
"I've had two and a half years with Hannover but I feel the time is right to come back to England and hopefully play a lot of games and do well for Stoke City."
"I'm very happy to be a Stoke City player because I'm joining a great club," he added.
"From the moment I walked through the door everyone was very welcoming and made me feel wanted.
"I've come here to try and improve my game, get better as a player and try to be a success. It's an exciting challenge for me.
"I can tell the fans of Stoke City I will always try and do my best and look to help the team improve and move forward.
"I'm looking forward to the start of pre-season and getting to know my new team-mates."
