Edwards described his decision to walk out at the Riverside to take charge at the Premier League's bottom club as "one of the toughest" of his career.
But the head coach says it was his "dream" to return to Wolves, where he has signed a three-and-a-half year deal as head coach.
Edwards signed a three-year contract at [Boro](https://www.thenorthernecho.co.uk/sport/football/middlesbrough/?ref=ed_direct) in the summer but left less than five months on, despite having repeatedly stressed the need for "unity" and "togetherness" on Teesside.
[Boro](http://www.thenorthernecho.co.uk/sport/football/middlesbrough?ref=au) will receive around £4m in compensation from Wolves, who are bottom of the Premier League and winless after 11 games.
Edwards is joined at Molineux by Harry Watling, whose Boro exit was also confirmed today. Adi Viveash is staying at the Riverside and will continue in charge of the first team while the process of appointing a new head coach is ongoing.
**RECOMMENDED READING:**
Wolves haven't yet published an interview with Edwards since his appointment earlier today, but the 42-year-old has posted on social media, attempting to explain his Boro exit.
A statement on his account said: "This has been one of the toughest decisions of my career. In truth, I wouldn't have considered leaving Middlesbrough for any other club.
"Wolves is a special club for me. It's where I grew as both a player and a coach, it's still where my family calls home. It has always been my dream to come back and these opportunities do not come around too often.
"Middlesbrough is an incredible club, with a fantastic owner, staff and passionate supporters. I want to thank everyone at the club for the opportunity to lead this squad. It is a great group of players that I genuinely hope and believe will deliver success this season.
"I could not be prouder of the environment we built together and how it all gelled together so quickly - the player, the staff, and the fans, who drive it all.
"I sincerely wish everyone at Middlesbrough all the very best for the rest of the season and beyond."
Edwards' first game in charge of Wolves will be at home to Crystal Palace a week on Saturday.