Wright, previously the Potters' academy manager and head of coaching and coach development, succeeds Terry Robinson, who left the club in the summer to take up a role as Leicester's director of football.
Wright told the club's website: "I am very much looking forward to the challenge.
"It's a great achievement what we have done so far and the important thing now is to maintain that Category One status, but also at the same time ensure that we are in a position to produce good young footballers.
"With Glyn Hodges now on board and his relationship to the first team - it is very much going to be that joined up process between the Academy and the first team with Glyn being the bridge between the two.
"The club are determined to make this work but it will take time and will need a period of continuity to let the programme run so that ultimately the process will be successful and bear fruit."
Stoke chief executive Tony Scholes was delighted to extend Wright's contract at the club for a fifth year and said: "Terry's departure gave us an opportunity to look at the Academy as it stands now as opposed to where it stood two or three years ago when Terry came in to take up his role.
"Terry did an excellent job and during his time with us Dave has developed his experience and knowledge of what is required to run a successful Academy.
"We've promoted him to the role of Academy Director and with him in place and Glyn Hodges as Senior Development Coach, assisted by experienced coaches in John Perkins and Jim Hunter, I think we have a really strong team in place."