Rams boss Paul Jewell began the rebuilding of his squad on Thursday by signing the 21-year-old Australia international on a two-year contract.
Zadkovich, who became a free agent after deciding to leave Sydney FC, was snapped up following an impressive spell on trial.
Zadkovich was easily convinced of Derby's potential and said: "Things haven't gone the way the club wanted this season.
"But everyone is looking to the future and I want to be a part of that.
"Now the team is relegated they can only start building as there is no point dwelling on the past - what has happened has happened.
"But this is such a massive club with great potential and we can only expect bigger and better things.
"I can only see them going back to the Premier League, which has to be the goal."
He feels he has matured as a player since his early days in England, adding: "I was very young then, and very inexperienced, but things have changed.
"Since then I have played a lot of international football with my age group and I've been called up to the national side, so I'm ready to play.
"There are points to prove, especially to some people, but I love a challenge and I'm ready for that."
Zadkovich will be given a helping hand by another Aussie at Derby in Mile Sterjovski, who joined in January.
Speaking to Derby's official website, Zadkovich added: "Mile has been such a big help and he is one of the reasons why I wanted to come here.
"He is such a nice person off the field and such a good player on it that I can only learn from him.
"To have a mate like that here, a fellow Australian, will be good for me.
"Obviously the facilities here are great, I saw that for myself, but Mile also spoke very highly of the club and gave me a lot of positive feedback."