The striker has been sold by Besiktas to Villa for £18.25m. The Black Eagles paid £11m to Roma earlier in the week to turn Abraham's loan into a permanent transfer before selling him onto Villa.
The 28-year-old has signed a four-and-a-half-year deal, having previously spent a year on-loan at Villa from Chelsea.
“It still doesn’t feel real,” Abraham admitted to VillaTV.
“Since this first time I arrived here, I fell in love with the club. Ever since I left this club, I’ve pretty much watched every game, so I’ve been keeping track.
“We had an amazing season (in 2018/19), amazing outcome, and I always told myself (that) if I had to come back to England, Villa would be one of the special teams to come back to.
“I spoke it into existence, so I’m happy to be here. So many great memories, and I'm here now to create even more.
“I just can’t wait to meet everyone, to be back at Villa Park and seeing the crowd and seeing so many familiar faces. It’s exciting.”
Excited to be back at Villa Park
Asked about the thought of running out at Villa Park again, he continued: “I don't think I can put that into words. I know it’s going to be emotional. Even though I only had a season here, it’s a club that means a lot to me, to my family as well.
“I think those are the pros about going away, learning different cultures and experiences. I feel like I left here as a boy and I’m definitely coming back as a man.
“I’d like to bring my experience to help the team as much as possible and achieve something with this club.
“I’ve played against most of the boys here, and I know a few of them also, so they’ve helped me settle in quickly.
“I just can’t wait to get out there on the pitch with them and make more memories.
“Right now, the world’s our oyster. We’ve got a good team, a good squad. I don’t think it’s out of reach to say we can push for every competition we’re in.
“I’m here and I want to win. I want to win trophies, so we have to push for every competition we’re in. I’m excited, I just can't wait.”