May joined Wednesday from St. Johnstone last summer, but he has struggled to make an impact at Hillsborough.
As a result, the Scottish club were plotting to make a loan move for the striker, as they wanted a reunion next season, but their efforts have proved fruitless.
Wright says that he was informed by Wednesday advisor Glenn Roeder that May will be a part of the Owls squad next season, as the side look to push for promotion out of the Championship.
“I know Glenn [Roeder] who is going in working in an upstairs role so we have been kept informed of what is happening with Stevie," he said.
“We threw our hat in the ring if Stevie was of a mind to come back north on loan but I think Stevie will be at Sheffield Wednesday next year."
May only managed to score nine goals in 45 matches this season, and his lack of goalscoring form became a source of frustration for some.
Although the 22-year-old frontman's pace and energy made him a dangerous outlet, his lack of cutting edge was a problem.
May will now be under pressure to have a better second season with the Yorkshire outfit and will be looking to prove that he can be a success in English football, having arrived last summer as a man billed as a hot prospect for the future.