The board believes that an orderly succession process will give a new CEO time to prepare the privatisation process and to lead the bank in the years that follow.
Hester said: "It has been nearly five years since I joined RBS after the bank was rescued by the government.
“In that time we have reduced the bank's balance sheet by nearly a trillion pounds, repaid hundreds of billions of taxpayer support, and removed the imminent threat that this bank's size and complexity posed to the UK economy.
“All the while we supported 30 million customers every day to help them manage their finances”
RBS now considers itself in a position where the government can begin to prepare for the privatisation of the bank.
Job cuts in its investment arm are expected to follow in the next 18 months which are widely reported to be in the region of 2000 losses worldwide some of which will be in the UK.
Hester, who was appointed to the board in October 2008, said: “While leading that process would be the end of an incredible chapter for me ideally for the company it should be led by someone at the beginning of their journey.
“I will therefore step down at the end of this year to allow a new CEO to lead the group in this next stage.”
The search for a successor will commence immediately led by Philip Hampton on behalf of the board, and will consider both internal and external candidates.
Philip Hampton, chairman of RBS, said: "On behalf of the board I would like to thank Stephen for his leadership and dedication over the past five years.
“In the midst of a major crisis, he accepted the challenge of stabilising the bank, turning it around, and putting us in a position where we can begin to plan for returning the organisation to the private sector. His achievements have been considerable”
At the point of Hester's departure, in line with his contractual arrangements, he will receive payment in lieu of notice of £1.6m representing 12 months pay and benefits.
He will not receive a bonus for 2013 which is also in line with contract terms.
