Rooney, who arrived at Pride Park as a player-manager in January last year, has signed a two-and-a-half-year contract.
The 35-year-old had been acting as Derby’s interim manager since November last year after Philip Cocu was sacked for non-performance, with the Rams bottom of the championship table.
Rooney lost just two of his nine games in temporary charge to move off the foot of the table and can leave the relegation places with victory over Rotherham this weekend.
Derby chief executive officer, Stephen Pearce, has told the club’s official website: “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 our 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 spent 13 years as a player at Manchester United, winning five Premier League titles, one UEFA Champions League, one FA Cup and three League Cups among numerous other honours.
He also enjoyed two spells at Everton and featured for D.C United in America’s Major League Soccer at the latter stages of his career.
Rooney is also England’s all-time top scorer with 53 goals from 120 caps.
Rooney said: "When I first arrived back in the United Kingdom I was completely blown away by the potential of Derby County Football Club. The stadium, training ground, the quality of the playing staff and the young players coming through and of course the fan base that has remained loyal and supportive.
"Despite other offers, I knew instinctively Derby County was the place for me.
"To be given the opportunity to follow the likes of Brian Clough, Jim Smith, Frank Lampard and Phillip Cocu is such an honour and 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."
