Christie has made the move to the East Midlands for an undisclosed fee, and manager Steve McClaren, who saw his side lose in the Championship playoff final in May, is delighted to add the 21-year-old to his first-team squad.
The 53-year-old told the club's official website: "We have been monitoring Cyrus for some time. He fits the profile of young, talented players. Right-back has been a focus for us this summer.
"We are delighted that Cyrus has chosen Derby County for this key stage of his career. There has been a great deal of competition for his signature."
Christie departs Coventry having made 116 appearances since his debut in 2010.