The 35-year-old former England captain has agreed a permanent deal until the summer of 2023, having succeeded Phillip Cocu on an interim basis in November.
An official Derby statement confirmed that, in accepting the manager's role, Rooney had "elected to call time on his illustrious playing career to fully focus on his job" and he retires having scored 53 times in 120 England appearances and won five Premier League titles at Manchester United.
"I can promise everyone involved in the club and all our fans, my staff and I will leave no stone unturned in achieving the potential I have witnessed over the last 12 months of this historic football club."
Rooney's professional career began at Everton, where he made his senior debut in 2002 aged 16. His first England cap followed at 17 and he lit up Euro 2004 in his first major tournament appearance before being sidelined by injury.
In the same summer he moved to Manchester United, breaking the record transfer fee for a teenager. He enjoyed great success at Old Trafford and is the only player to have scored more than 250 goals for the Red Devils, eclipsing Sir Bobby Charlton's record in 2017.
That same year he returned to Everton, before moving to DC United in 2018.
Rooney was never able to replicate his displays at Euro 2004 at a future tournament and was sent off during England's World Cup quarter-final defeat to Portugal in 2006.