Wayne Rooney won 24 of his 85 games in charge of Derby County, with 22 draws and 39 defeats
The 36-year-old's contract with the club had another year to run.
The Rams have been in administration since September last year and were relegated to League One last season.
"I feel the club now needs to be led by someone with fresh energy and not affected by events that have happened over the last 18 months," he said.
The former Everton, Manchester United and England forward said he had been "closely following developments" regarding the ownership of the club and informed joint administrators Quantuma of his decision at a meeting on Friday when they tried "tremendously hard" to change his mind.
"My time at the club has been a rollercoaster of emotions, both highs and lows, but I have to say that I have enjoyed the challenge," Rooney added.
"I will remember my time at Derby with great pride and affection and would like to thank all my staff, players and of course the fans for their incredible support. I will never forget you and hope to see you all again in the near future and in happier times.
"Finally, I am aware that the club still have interested parties who wish to take over the running of the club. To them I say this, Derby County is a great club with a great history and great fans. I wish you all the best and much success for the future."
The news came on the same day that property developer David Clowes announced a bid to buy the club after purchasing Derby's Pride Park stadium.
His company Clowes Developments (UK) Ltd, have also given a loan to the club to allow them to start next season.
It followed the collapse of US businessman Chris Kirchner's takeover plans on 13 June - a bid which Rooney had publicly backed in April when he was confirmed as the preferred bidder.
Derby will be playing in the third tier of English football for the first time since the 1980s following relegation
Derby are due to play Oxford United in their opening League One game on 30 July, but are still subject to an English Football League embargo and only have five senior players under contract.
In a statement, Quantuma said: "The joint administrators are very disappointed that Wayne has taken the difficult decision to leave the club and we have spent some time today trying to persuade him to stay but understand his reasons for wanting to go.
"We are extremely grateful to him for his excellent work in the face of challenging on-field circumstances in the 2021-22 season and admire the manner in which he has led the team, the club and the local community through various off-field issues.
"The joint administrators recognise that staff and supporters will be frustrated and equally disappointed by this news, but we all wish him, his wife Coleen and their four boys every success in the future and we are sure they will always be welcomed back."
They added, however, that Rooney's decision to leave would not affect "ongoing, positive discussions" about the sale of the club.
Wayne Rooney made his Everton debut at the age of 16 and later won 16 trophies with Manchester United
Rooney, England's record goal-scorer with 53 goals in 120 internationals, joined Derby as a player in January 2020 following a spell in US Major League Soccer with DC United.
He was put in interim charge of the team in November of that year - his first job in management - with the club bottom of the Championship after they parted company with Phillip Cocu.
Rooney was confirmed in the post on a two-and-half-year contract three months later, a decision which prompted him to confirm his retirement as a player.
He managed to keep the Rams up by virtue of a 3-3 draw with Sheffield Wednesday on the final day of the 2020-21 season, having twice been behind in the game.
But former owner Mel Morris' decision to place the club into administration and breaches of EFL financial rules meant Rooney was hamstrung last season by the deduction of 21 points, and a transfer embargo.
Derby eventually finished next to bottom, seven points from safety. Had the points deductions not been imposed, they would have stayed up in 17th place.
Rooney's dignity and close bond with his players and staff won him countless admirers among Derby supporters, which led to him being linked with other jobs at former club Everton and Burnley.
And last month councillors took the still-to-be-ratified decision to grant him the freedom of the city for his "great commitment" to the city and for "galvanising and revolutionising" the Rams fanbase.
The club must now begin a search for his successor, at the same time as trying to conclude a takeover deal that will secure their future.
-- Courtesy of BBC Sport