Webber will report to recently-appointed head of football development and recruitment Kevin Thelwell as the club continue their restructuring process.
"I am delighted that Stuart has joined the club," Wolves manager Stale Solbakken said.
"It is part of the new structure put in place with Kevin Thelwell and is an important appointment which will benefit us in the transfer market both at home and abroad."
Webber has previously worked with Wrexham, Liverpool and QPR and he is delighted to be at Molineux.
"It all happened quite quickly but I'm excited to be here and really looking forward to the challenge," he said.
"With Kevin's change of role and the club looking to go in a slightly different direction it is a good opportunity and an exciting one, although there is a lot of work to do.
"The guys that have left did a very good job but now we have to put our own stamp on it and take things forward.
"We need to have a good network of scouts in operation not only in England but also further afield and we need to bring the department up to speed with modern day football.
"There are so many more resources available now than there has ever been and it is about utilising those to get the best for this club.
"That means identifying good players at good value to help the club develop and get back to where we want to be which is ultimately the Premier League."