Edwards leaves Middlesbrough following a fast start to the Championship season, with the Teesiders second in the league.
The Welshman returns to Wolves having spent four years there as a player, making 100 appearances for the club before becoming an under-18s coach.
Wolves executive chairman Jeff Shi said the club is in need of an extensive "refresh", with Edwards' philosophy set to be at the heart of the process.
Shi said: "I know Rob very well and I have seen his growth in different jobs. He's a very good person, he knows the club very well, he knows the city, the fans and he is very talented.
"When he was a youth coach here, he showed his tactical awareness, but after he took first-team jobs he started to grow his own identity, character and leadership.
"We need to refresh the whole club with a new coach's philosophy, bringing his own identity and ideas, and we can build on that. We are at a new chapter for the club and Rob will be a key piece of that."
Edwards worked his way through the coaching system to become interim manager for two games in 2016 and would eventually leave for hometown club Telford.
A successful stint at Forest Green - where he won promotion and Manager of the Season in League Two - prompted attention from Watford, where he fell victim to the constant managerial changes seen at Vicarage Road.
Less than two months after being sacked by the Hornets, Edwards was hired by rivals Luton and oversaw promotion to the Premier League via the play-offs for the first time in the club's history.
Relegation followed in the next campaign, but the Hatters stuck with him upon their return to the Championship, only for him to leave by mutual consent after a torrid start to the season, and Luton would eventually suffer back-to-back demotions.
Edwards was appointed Middlesbrough manager in June 2025 and has guided them to second in the Championship, prompting Wolves to bring him back to the club nearly a decade after departing.