Delap, now 35, has been with the Potters for six seasons since he signed from Sunderland for £500,000.
Since then he has made over 200 games for City.
Manager Tony Pulis told the club’s official website: "Rory deserves this deal. It is important we look after those players who have been here since the start of this journey.
"It's not just what he does on the field; he's been an inspiration off the pitch as well.
"He has played close to 600 games during his playing career, and the vast majority of those have been in the top-flight and so he has offers so much more than just a long throw.
"He is the ultimate professional and it is important we look after certain players at the football club who started all this off."