Edwards left the Bucks last month after a season in charge, guiding them to a 14th-placed finish in National League North.
Sean Parrish will be his assistant, having also served in the role at the New Bucks Head, while former Under-23s chief Scott Sellars has become head of academy player development.
Wolves academy manager Gareth Prosser said: "Rob Edwards has come through a recruitment process and we are delighted to welcome him back to the club, as our Under-23 lead coach.
"He will be assisted by Sean Parrish and the rest of the performance team and will be tasked with leading the Under-23s on a daily basis.
"Rob has the development of players at the heart of everything he does.
"I am sure he will fit back into the club very quickly to continue the development of our young players.
"There is no doubt the standard of football at this club has risen in the last 12 months and we all have the responsibility to ensure our players hit these new standards."
Edwards, from Madeley, spent four years with Wolves as a player – from 2004 until 2008 – and made 111 appearances.
The 35-year-old former defender also played 15 times for Wales, and had a stint at Shrewsbury Town.
He has been under-18s coach, first team coach and interim head coach at Wolves too.
Edwards took five Wolves players on loan deals at Telford last term – Aaron Hayden, Aaron Simpson, Connor Johnson, Ryan Leak and Ryan Giles.
Wolves sporting director Kevin Thelwell said: “Rob is someone we’ve known for a while, following his time as a player and more recently as a coach for the academy and with the first team.
“He will be a perfect fit and he is someone who will help to continue help our young players develop.
“Scott has done an excellent job leading the Under-23s group over the last few years and his new position will allow him to flourish even further.
“I am looking forward to seeing how our Under-23s progress in the forthcoming season.”