Kitson has become Tony Pulis' first summer signing and has signed a three year deal. Kitson has cost Stoke £5.5m. He scored 54 goals in 111 games for Reading. A fair record for any striker.
Steve Coppell said, "Dave was one of my first signings and I'd like to thank him for his contribution over the last four and a half years.
"I am sad to see him leave but it was his wish to play in the Premier League and Stoke have offered that avenue.
"We wish him the best of luck but his departure will open the door for the players who remain to demand a consistent role in the team."
There is no sell-on clause to Cambridge and Royals director of football Nick Hammond added, "Once Steve 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.
"This has been achieved and the money is now available for Steve to strengthen the squad as and when he sees fit."