He admits playing the second-half of the season with a pre-contract was tough.
Wilson, 25, said: "When you've signed a pre-contract your mind and heart is with the other team.
"I tried to make that clear to Forest. I'm a Nottingham boy, a Forest fan, and I wanted them to do well but it was time for me to move on.
"I didn't go to Forest and ask them to let me leave. I left it to the two clubs because I knew I was coming in the summer.
"I'd have loved to have been a part of it but things don't always go to plan.
"I was carrying a few niggles at Forest and the team was doing really well. There was no point risking the injuries and I'd signed the pre-contract.
"For both parties it was right for me not to play. I got on well with Billy all the way through.
"He signed me at Preston and there's never been a problem. He never had a go at me and there were no arguments. He wished me well when I signed the pre-contract.
"Without him and Colin Calderwood, who gave me that chance to get away from Preston and play football at Forest again, maybe I wouldn't be sitting here.
"I said I'd only leave Forest to go to a bigger club and in joining Celtic that's what I've done."