The 42-year-old former defender and youth coach joins from Championship outfit Middlesbrough for his second crack at Premier League management.
Edwards has agreed a three-and-a-half year contract at Molineux as he arrives tasked with lifting the top flight's bottom club off the foot of the table.
Telford-born head coach Edwards begins a fourth spell at Wolves, where he spent four seasons as a player until 2008 and coached, initially with the under-18s before a return at under-23 level.
He was stood down from the last game at former club Boro, in which the Championship high-flyers went on to beat Birmingham 2-1.
Edwards will be joined by assistant head coach Harry Watling, who was deputy for the new Wolves boss in Teesside. More members of Edwards' backroom team are due to follow.
Wolves are believed to have paid a compensation package of around £2million for the appointment.
Edwards, a promotion-winner with Forest Green and Luton, can "refresh the whole club" as Wolves begin a "new chapter", according to executive chairman Jeff Shi.
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.”