Edwards signed a three-and-a-half-year contract with bottom side Wolves after they agreed terms with high-flying second-tier team Middlesbrough, who initially rejected an approach before they reluctantly released Edwards after just 15 games in charge.
"I know I was in a great job at Middlesbrough. Great people and very good players who have done well, so I'm aware of it. But this is something I have wanted to do for a very, very long time," former Luton Town boss Edwards told reporters.
"I didn't know if this opportunity would come up again for me to be the head coach of this club. I didn't want to look back in 10, 15, 20 years' time that I turned down the chance to manage Wolves in the Premier League. That's it.
"I didn't want to regret that and here I am. I know the scale of the task and I'm really enthused by it. This week has been really enjoyable, but now the games start. So let's see."
'Genuinely proud'
Edwards, a former youth team coach and player at Wolves, said the pull of returning to Molineux was irresistible despite the daunting challenge ahead, with the 42-year-old adding he was "genuinely proud" to return to the club.
"It feels amazing to be back... I will not lie, it has been an aim of mine since I got the under-18s job. Something I've always wanted to do," Edwards added.
"There's no perfect job in football. I know the scale of the task. But also really excited by the challenge as well and I've got full belief in the group."
Wolves, who host Crystal Palace on Saturday, are stranded at the bottom of the standings without a win all season, their Premier League survival in serious doubt.
'Enough time'
Wolves are eight points from the safety zone but Edwards insisted he will not dwell on their precarious league position.
"I'll be clear with players, this is what we are going to do and how to win games of football and get points. It's going to come from hard work," he said.
"We will support them as well and we believe in them. I've told them that. We can't look too far ahead and where we are with the gap at the moment.
"There is still enough time. I understand we want to get results quickly as well as that will help with that belief."