The 23-year-old striker, who had a spell on loan at the City Ground last season expressed his delight on making the move permanent.
"I'm very happy to be back. It's nice to see the lads, the manager and the staff again and I can't wait to get back in the swing of things," he told the club's official website.
"I enjoyed everything about my time with Forest last season. We were in the relegation zone and ended up surviving quite comfortably in the end and didn't lose in my time at the club.
"I was really happy with the way things went. I've had a taste of what this club is all about and now I want more."