He signs off after overseeing a triumph on penalties in the EFL Trophy at Morecambe on Tuesday night.
Ex-Wolves winger Mark Kennedy, who had been assisting Edwards and Sean Parrish in coaching the side, has been placed in caretaker charge.
"Whilst it is always disappointing to lose such a talented coach and highly valued member of our backroom staff, we’re proud that Rob has been offered such a prestigious role at the FA to help develop the best young talent in the country," said Wolves' sporting director Kevin Thelwell.
"We’ve been delighted with the work Rob has done, not only with the under-23s and last season’s fantastic PL2 Division 2 title-winning campaign, but with the whole professional phase of the academy.
"We would all like to wish Rob the very best in his new venture and thank him for his considerable contribution to Wolves and to the academy.
“We will now be looking to identify a suitable successor who has the hunger, vision and drive to lead our under-23s during one of the most exciting periods in the club’s history.”
Edwards, who made more than 110 appearances in gold and black before serving the club in various coaching positions, added: "I’ve had so many roles at Wolves during different stages of my career, that I feel like it’s my club now.
"I love this club, but this is the right time and the right opportunity to take.
"I wish the club all the best going forward in what I know will be a very successful future.”