Kitson signed for the Royals from Cambridge United for just £150,000 in 2003 and was one of Reading manager Steve Coppell's first signings.
Reading director of football Nick Hammond believes the Royals have got a good price for Kitson.
"Once Steve Coppell had decided that it was in the Club's best interests for the deal to be done, it was my task to generate the maximum income," Hammond told the Reading website.
"This has been achieved and the money is now available for Steve to strengthen the squad as and when he sees fit."
Coppell added: "I'm sad to see him leave but it was his wish to play in the Premier League and Stoke have offered that avenue."
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