Fairhead was appointed to take over as chair of the new BBC management structure when it launches next year by David Cameron before the referendum. However, pressure over the decision, which was taken following a meeting with the former Prime Minister, has mounted over the summer.
Read more: What we learned from the BBC annual report
This afternoon, Theresa May told the BBC it will run a new process to appoint the first ever chair of a unified BBC board, the role Fairhead would have taken over next year when the BBC Trust is scrapped.
Fairhead, who became chair of the Trust in October 2014, announced this afternoon she would not be reapplying for the role. She said: "I took on the leadership of the Trust to help stabilise, strengthen and develop the BBC following a very difficult period in its history.
"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."
Read more: White paper stops short of "castrating" BBC
Fairhead will stay on as the last ever head of the Trust until next year, when the Trust is replaced by a unified BBC board. She added: "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."
BBC director general Tony Hall said: "Rona has made a real contribution to 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."
A spokesperson for the Department for Culture, Media and Sport (DCMS) said: "The Government thanks Rona Fairhead for her service to the BBC. Full details of the BBC Charter will be announced shortly.”