Chairman of the BBC Trust Rona Fairhead is to step aside after two years in the role, the organisation has confirmed.
In a statement Ms Fairhead said she decided to quit rather than take part in the reapplication process for the role.
She said: "The Prime Minister strongly encouraged me to take part in the new appointment process, for what would be a new four year term as BBC chairman.
"However, after much thought I have come to the conclusion that I should not do so.
"It is my belief that it will be better to have a clean break and for the Government to appoint someone new, and for me to continue my career in the private sector as I had always planned to do after my existing term ended in 2018."
Ms Fairhead has held the role since October 2014.
In May, following the publication of the BBC White Paper, she was asked to continue in the role for four more years by David Cameron's government.
She will remain in the role until someone is appointed chair of the new board, which will replace the trust.
Announcing her resignation, she said: "I took on leadership of the Trust to help stabilise, strengthen and develop the BBC following a very difficult period in its history and through Charter Review. I was always clear that I was willing to serve for four years, after which I would continue my career in the private sector.
"I am proud of what I and my colleagues, both at the Trust and the BBC, have accomplished during the past two years. I believe the draft Charter will secure the strong, confident and independent BBC that the public want and deserve.
"The BBC is a wonderful organisation and I have huge confidence in its future. I wish the new chairman, the board and everyone at the BBC every success.
"The Government and the BBC will have my full support in transitioning to the new governance arrangements to ensure the BBC remains the bold, creative institution that is loved and admired by so many."
Ms Fairhead was chief executive and chairman of the Financial Times Group between 2006 and 2013 and has also held senior roles in financial and global business.
A Number 10 spokesman declined to comment.
BBC director-general Tony Hall said: "Rona has made a real contribution to the BBC and at a really important time for us.
"On behalf of all the staff, I'd like to thank her for that and wish her the very best for the future. We will continue to work together in the interests of licence fee payers until the new governance arrangements are in place."