BBC Trust chairman Lord Patten is standing down from the role with immediate effect on health grounds following major heart surgery.
He said he was leaving "on the advice of my doctors".
Lord Patten, a former Conservative Cabinet minister, also served as the last governor of Hong Kong.
In his time at the Trust, he has faced criticism for doing the job while holding a number of other roles in the public and private sector.
Lord Patten, who had heart surgery while in Hong Kong, said he underwent further surgery last month after being admitted to hospital with "serious chest pains".
He paid tribute to the medical staff who treated him, saying: "On the advice of my doctors, however, and having consulted my family and friends, I have concluded that I cannot continue to work at the same full pace as I have done to date, and that I should reduce the range of roles I undertake.
"On this basis I have decided with great regret to step down from much the most demanding of my roles - that of chairman of the BBC Trust. This is a position that requires and has received from me 100%, and has been my priority at all times. It would not be fair to my family to continue as before; and equally it would not be fair to the BBC and those it serves not to be able to give that commitment which the role demands. I have to begin by taking a six-week break from any work at all."
His departure comes as the BBC faces further fallout from the Dame Janet Smith review into the corporation's "culture and practices" while disgraced DJ Jimmy Savile worked there.
Lord Patten said: "It has been a privilege to have served as chairman of the BBC Trust. Like the NHS, the BBC is a huge national asset which is part of the everyday fabric of our lives. It is not perfect - what institution is? It always needs to challenge itself to improve. But it is a precious and wonderful thing, a hugely positive influence which benefits greatly from the creativity and dedication of its staff.
"I have had no reason to doubt that the leaders of all main political parties support the role it plays at the centre of our public realm. Most important of all, the British public enormously value the strength of its output, its independence and the contribution it makes every day to the quality of our lives.
"When in due course the future of the BBC is subject to further discussion at Charter Review time, I hope to say more on the issue. For the time being, however, I shall be making no further statement whatsoever about the BBC or my period as chairman of the BBC Trust."
Vice-chairman Diane Coyle will take over as acting chairman until a successor is appointed.