Hester, parachuted in during the 2008 banking crisis, did not want to remain for another five years to see through the return of the 81% government stake back to the private sector.
"We are now in a position where the government can begin to prepare for privatising RBS. 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," Hester said.
Describing the role as "bruising and difficult" Hester added: "It is a sensible thing for the board to look forward to privatisation and I can completely understand that a fresh face with an ability to commit many years into the future may be a good thing for privatisation."
After he leaves he will receive £1.6m in pay and benefits and up to £4m in awards of long-term incentive plans over the following three years.
Sir Philip Hampton, the chairman of RBS, thanked Hester. "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," Hampton said.
Hester's resignation comes amid speculation that the chancellor will use next week's Mansion House speech to signal a privatisation plan for both RBS and Lloyds Banking Group.
Osborne said Hester had "made an important contribution to Britain's recovery from the financial crisis".
"Having brought RBS back from the brink, now is the time to move on from the rescue phase to focus on RBS being a UK bank that provides greater support to the British economy, helping businesses and job creation here, and which can return to the private sector in a way that ensures value for the taxpayer," Osborne said, confirming he would use the Mansion House speech to say more "on reform of the banking system".
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