The 38-year-old – who also featured for Wolves and Villa in a 14-year playing career – spent several years at Molineux as a under-18, under-23 and first team coach. He also had a short spell as interim manager when Walter Zenga was sacked.
He left Wolves in 2019 to become a coach for the England under-20 team and a year later he also became head coach for the England under-16s.
Now, Edwards has made the switch to League Two and becomes the new head coach at Rovers – who recently lost in the play-off semi-finals. He will be assisted by Richie Kyle.
Edwards said: "This is a club that feels really different from others – and actually does things another way.
"My conversations with the chairman were incredibly positive, and showed we’ll get the time and support we need to go on a winning journey.
"The club has a well-developed footballing infrastructure under Richard Hughes, and with great people behind the scenes and incredible fans, I’m looking forward to getting started."