The struggling Championship club said in a statement that the 35-year-old had signed a two-and-a-half-year contract.
Rooney, who scored an all-time record 53 goals for England and is also Manchester United's record scorer, joined Derby in a player-coach capacity a year ago from MLS side DC United and made 35 appearances for the club.
He had been interim manager at Derby since the club parted company with Dutchman Phillip Cocu in November.
Rooney began his playing career with boyhood club Everton, scoring his first goal in spectacular fashion as a 16-year-old against Arsenal.
He became one of the country's most iconic players, scoring 253 goals for United and winning five league titles and the Champions League. Rooney is also England's most capped outfield player, with 120 international appearances.