Stevens was out for more than three months at the turn of the year because of calf and hamstring injuries but returned to the side at the end of March to help steer the Potters to safety as they finished 17th, six points clear of the relegation zone.
“We finished last season strongly and Enda played his part in that,” said Stoke sporting director Jonathan Walters.
“He brought quality to our side with and without the ball, as well as the wisdom of having seen everything there is to see at this level, and that helped us immensely in those high-pressure games.”