Chadwick burst onto the scene last year scoring three first team goals for Everton, but he has missed most of this year with a hernia problem.
Chadwick said: "This has been a nightmare season for me and I need to go forward now. I'm here at Derby trying to find my game again, I'm determined to make a go of it and I'm determined to play well."
Chadwisk made his debut for the Rams during their 1-1 home draw with Leicster on Saturday.