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.
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However, the 26-year-old striker returns after a successful stint in Germany, where he scored 26 goals in 57 Bundesliga appearances for Hannover and he believes that he is now ready to shine in the Premier League.
"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."
Diouf went on to say he already feels at home at the Britannia, and cannot wait to get started at his new club.
"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."