The 35-year-old retires as the all-time leading goalscorer for both Manchester United and England.
Derby CEO Stephen Pearce added: "We are delighted to confirm the appointment of Wayne Rooney as our new manager.
"Our recent upturn in results under Wayne was married together with some positive performances, notably the 2-0 home win over Swansea City and the 4-0 victory at Birmingham City.
"During that nine-game run we also dramatically improved their defensive record and registered five clean sheets in the process, while in the attacking third we became more effective and ruthless too.
"Those foundations have provided a platform for the club to build on in the second half of the season under Wayne's guidance."
Rooney's first game as permanent manager will be on Saturday at home to Rotherham at Pride Park.
It has been a time of turmoil for Derby, with the senior first-team players still waiting for their December wages to be paid.