The pair worked together during Edwards' previous time at Wolves, while also when the latter was manager of Forest Green Rovers.
Hayward told the Wolves website: "Rob is someone that we know well at the club and someone who I've personally worked with before, both here and elsewhere. I think he's going to be a great appointment for the club and hopefully can help get us back on track and inject a lot of positivity and energy into the playing group, and also the staff and everyone around the club. I think he can really help with that energy, that positivity.
“The big thing about Rob is his personality, his people skills, his enthusiasm, his ability to really get the most out of people, not just the players, but the staff as well. I think people really want to work hard for him, because he creates a good connection on a personal level, and because of that interpersonal connection that he establishes with people, it naturally motivates them to want to work harder and want to help him, and that's going to stand him in good stead here, initially with the players, but also with the staff at Compton.
“There's definitely a lot of excitement here amongst the staff, both ones who've known and worked with him before, but then also ones who haven't have heard good things about him from his time here before. I think a lot of people are excited to get working with him.
“Everyone's going to want to do absolutely everything they can to try and get the most out of this playing group, to try and get us where we need to be, which is obviously a lot higher up the table than we are at the moment. Everyone's going to be pulling together to make sure we're giving everything we can to get this thing turned around.”