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'We are pleased that Peter has signed. After two years here he has now adjusted to English football and its demands,' director of football John Rudge told the club's official website. 'Added to that, he has that extra bit of quality and skill you need in Division One to change a game.'
Chairman, Gunnar Thor Gislasson said: "I want to put on record our gratitude to Peter for showing the desire to continue to do well for Stoke.
"But not only just that - I also pay tribute to him for recognising the economic realities which football is now facing.
"Reduced salaries for footballers is not only an English phenomenon, but a European one. They must understand that a reduced offer is not a reflection on their abilities as a footballer, but a reflection of the new financial realities in football."
Manager Tony Pulis, meanwhile, has hailed Hoekstra's decision to accept a new one-year deal, stating: "It's fair to say the two of us have had one or two moments when we haven't seen eye to eye, and he is a high maintenance player requiring close attention to his fitness.
"But I happen to think he's worth that attention because I have terrific respect for his exceptional technical ability, his first-class attitude to training and the fact the younger lads look up to him."
Gunnarson, Clarke, Hall and O'Connor are still considering offers.