The midfielder has left Sheffield United for Derby, five years after leaving Forest.
"It’s been five years since I left Forest. I left on OK terms,” he told Rams TV. “I carried on wanting them (Forest) to do well when I was at Sheffield United. They gave me everything, really. They picked me up when Derby let me go and gave me a career. I owe a lot to them as a club and the people there especially. It’s all about the people, really, rather than the club.
“I think most will understand my decision in coming here. There is always going to be a stick and rivalry because it is what it is.”
Osborn continued: “My dad was a huge Derby fan his whole life. When I went to Forest things got a bit messy for him.
“He unfortunately passed away a couple of months ago. It’s been emotional that he’s not seen me play for Derby.”
He added: “I played here when I was really young, got released and went to the other side of the A52 for a number of years but still remained a Derby fan until I started getting close to the Forest first-team. It all got a little muddled up then! I’ve gone full circle, it’s been emotional but I’m really excited to get going.”