Edwards, 42, leaves Championship side Middlesbrough, where he had been in charge since June, to take on the task of guiding the Premier League's bottom club.
The Midlands side, winless in the top flight with just two points from 11 games, are currently eight points adrift of safety after Saturday's 3-0 defeat at Chelsea. Edwards will be joined at Molineux by Harry Watling, also moving from Middlesbrough to become assistant head coach, with further backroom appointments expected soon.
Edwards has a long-standing connection with Wolves, having made 111 appearances as a player between 2004 and 2008. He previously worked within the club's coaching system, starting with the U18s in 2014 before progressing to the first team in 2015 and eventually becoming head coach of the U23s in 2019.
His managerial career includes guiding Luton Town to the Premier League in 2023 and a stint at Watford. Middlesbrough, meanwhile, continue to push for promotion in the Championship, finishing second in the table under his leadership prior to his departure.
Wolves executive chairman Jeff Shi expressed confidence in Edwards' appointment, saying: "Rob knows the club, the city, and the fans very well. We need to refresh the whole club with a new coach's philosophy, bringing his own identity and ideas. We are at a new chapter for the club, and Rob will be a key piece of that."
The 42-year-old was absent from Middlesbrough's dugout for their 2-1 win over Birmingham City last weekend after being granted permission to speak to Wolves, following initial resistance from his former club. Edwards now faces the immediate challenge of reversing Wolves' fortunes and steering them clear of relegation.
