The 42-year-old has left Championship club Middlesbrough and agreed a contract until 2029 with Wanderers after they sacked Vitor Pereira earlier this month.
It is reported Boro will receive around £3million in compensation after Edwards only joined them in June on a three-year contract.
Edwards' penultimate game at the Middlesbrough helm proved to be their 3-0 defeat at Vicarage Road at the start of this month when he returned to the club for the first time since he was sacked after just 11 matches of the 2022/23 season.
The new Wolves head coach will be hoping he can change the club’s fortunes around after nine defeats from their opening 11 matches has left them sitting eight points adrift of safety in the Premier League.
His first game in charge will come after the international break on November 22 when Wolves play at home to Crystal Palace.
Edwards, who managed Luton in the Premier League, begins a fourth spell at Wolves after making 111 appearances as a player as well as enjoying time as a coach and interim boss.
He will be joined by assistant head coach Harry Watling after the pair worked together at Middlesbrough, with the rest of his backroom staff to be confirmed in the near future.
Wolves chairman Jeff 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.”