Henderson has joined the Blades on-loan for the season.
"We've know a lot about Dean for the last two or three seasons really and we've tracked his progress," Wilder told the Sheffield United website.
“He was the outstanding goalkeeper in the EFL last year in my opinion. We met him and spoke to people he's worked with and played with, in addition to having watched him consistently last season.
“And we're delighted he sees his immediate future here with us, not only an outstanding young goalkeeper, but he has a fantastic attitude to improve himself and be involved in hopefully a successful club in the Championship."