Edwards left Middlesbrough less than six months into his job to return to Molineux, where he both played and worked as a coach for Wolves.
With Boro furious over Edwards' actions, the new Wolves manager told the club's website: “It means a lot. This club’s really special. It’s special anyway, but it’s special to me because it’s where I’ve spent most of my professional career and where I played most of my football.
“Then to have done a lot of the roles that I’ve done, I’ve got to be honest, this job was always my aim. This is the dream.
“I know the situation that we’re in right now, but this is just something that I’ve always wanted, and I’m ready for it. I’m ready for the challenge, I’m up for it, and it’s been great getting around everybody, seeing so many faces that I know, and new faces as well.
“The staff are all up for it and we’ll meet the players next week when everyone arrives back, and I know the lads will be as well.”
Wolves currently sit bottom of the Premier League table, but Edwards is confident leading the team out of the dropzone.
He also stated: “Jeff (chairman Jeff Shi) talked to me about a reset moment. It’s an opportunity for us now and I know we’re in a difficult spot, but there are still 27 games to go, so there’s an opportunity here for us to do something really special, and that appeals to me.
“I’ve always been a risk taker and I’ve always wanted this job, and you don’t know if it’s ever going to come along again, and the opportunity was there right now. It’s going to be difficult, but there’s an opportunity for us to maintain our Premier League status this year and then grow and continue to grow and build as well.
“It’s not quite gone our way so far this season, but that has got to be done. Now, it’s about moving forward and what we can do to affect it, and that’s working incredibly hard, leaving it all out there to try and drag our way out of it.
“Short-term, that’s got to be our aim; we’ve got to try and find results, and in the long-term, let’s look to try and build something again, build on our identity and a connection with everybody again. Those have been the conversations and I’m just relishing the opportunity.”