Edwards has left Championship club Middlesbrough and replaces Vitor Pereira, who was sacked by Wolves earlier this month.
The 42-year-old, who managed Luton in the Premier League, faces a huge task to extend Wolves’ eight-year stay in the top flight.
Wolves have taken just two points from their opening 11 league games, losing nine times to sink to the bottom of the table.
Edwards will be in his fourth spell at Wolves after making 111 appearances as a player, as well as enjoying time at the Midlands club as a coach and interim boss.
“I know Rob very well and I have seen his growth in different jobs,” said Wolves chairman Jeff Shi.
“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.”
Edwards lifted Middlesbrough to second place in the Championship table, five points behind leaders Coventry, prior to his departure.
Wolves are already eight points from safety and Shi added: “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.”
Middlesbrough had initially rejected an approach for Edwards, who only joined the club in June.
Edwards, however, expressed his desire for a move to Molineux and was stood down for Middlesbrough’s Championship win against Birmingham on Saturday after the clubs agreed a reported £3 million compensation package.
He will be joined by assistant head coach Harry Watling after the pair worked together at Middlesbrough
Edwards’ first game in charge of Wolves will come after the international break on Nov 22, at home to Crystal Palace.
He arrives at Molineux tasking with lifting a gloomy atmosphere after frustrated fans turned on Pereira and called for owners Fosun to sell the club.
Pereira had saved Wolves from relegation last season but the Portuguese coach was unable to recreate that magic this term.
Confidence has been at rock bottom for much of the season, with successive 3-0 defeats at Fulham and Chelsea in their last two matches providing the impetus for Shi to take the managerial change.