The 27-year-old defender rejoined Forest on Friday after signing a three-year deal at the City Ground.
Wilson, who had played for the Reds between 2007 and 2011 before joining Celtic, has said that it feels good to return to the club.
"It's nice to be back. I'm delighted to get it all sorted and I can't wait to get started to be honest," he told Forest's official website.
"I wouldn't have left Celtic for just anyone, it had to be the right club. And no club fitted the bill better than Nottingham Forest.
"I've been at Notts County, Preston and Celtic but looking back and trying to pick a spell I enjoyed the most, even though I played in the Champions League with Celtic, I would have to say it was here."
Wilson could feature in Forest's match against Blackburn Rovers on Saturday.