His departure is intended to clear the way for what will be one of the biggest ever public sell-offs.
The business secretary, Vince Cable, who opposes a rapid sale of the taxpayer's 81% stake, said the bank needed to focus more lending to small businesses and supporting the economy.
"He performed a necessary role at a difficult time," said Cable of Hester. "Going forward RBS needs more of a focus on SME [small and medium-sized firms] lending and supporting the economy."
Conservative MP David Ruffley told Sky News: "Politics has interfered in what should have been a pretty simple business decision." It looked like "more than coincidence" that Hester was leaving when politicians had their "sticky little paws" over the future of RBS.
As expectations faded that George Osborne would use next week's Mansion House speech to set out a definitive course for RBS's privatisation, the bank's chairman Sir Philip Hampton, insisted that a sale of the stake, for which taxpayers paid £45bn, could begin at the end of 2014.
Treasury sources described Hester's departure as by "mutual agreement" and were cautious about the timescale of any sell-off of a bank which has 30 million customers and is one of the biggest lenders to households and businesses in Britain.
Osborne, who has refused to indicate when and how he wants to return RBS to the private sector, said that it was now time to "move on from the rescue phase to focus on RBS being a 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".
"I want to commend Stephen Hester for everything he has done to make this turnaround possible. The size and complexity of the bank has been significantly reduced, with a far greater focus on serving its UK customers."
The report from the parliamentary commission on banking standards, due in the coming days, is expected to influence the chancellor's thinking. Lord Lawson, the Tory peer who sits on the commission, wants to break up RBS into a good and bad bank though, it is unclear whether all the 10 commission members will back his call. Analysts at the Policy Exchange thinktank have warned such measures could delay privatisation.
Analysts were surprised by Hester's departure. In recent weeks he had made it clear he wanted to stay in his job to see the return to the private sector after joining the bank at the time of the 2008 bailout.
Ian Gordon, analyst at stockbrokers Investec, described Hester's departure as a "highly regrettable development for all RBS shareholders". "Hester has done a commendable repair job … but his departure raises fresh uncertainty at a time when RBS remains, at best, marginally profitable with a very weak outlook for earnings and returns," said Gordon.
But analysts at Bernstein Research said they thought Hester's departure was a positive development as his clean-up operation of a bank that was making £24bn losses in year must be complete. "The UK government (the perfect insider) wouldn't have let Hester go if there was still derisking to be done in the bank – especially given the fact that he was absolutely key in turning around the bank and that over a prolonged period of more than five years and under extreme political duress."
The starting pistol is now being fired on appointing a successor to Hester. The 52-year-old career banker has almost seen through his five-year restructuring plan though it has been forced to undergo changes as a result of regulatory and political pressure.
The US arm, Citizens, is being prepared for flotation by Bruce van Saun, the finance director, who might have been regarded as potential candidate to take the top job. Hester was also forced to scale back the investment bank more than he had originally intended and a further 2,000 jobs are expected to be announced in that division on Thursday.
Lord Oakeshott, the Liberal Democrat peer who is outspoken on the banking industry, said Hester's successor should not focus on privatisation. "The Treasury must install a successor to get desperately needed loans out to small businesses for investment and jobs, not flog the shares off for a song," he said.
There was speculation that the board wanted an appointment from outside but new recruit Ross McEwan, who runs the retail bank, and the new finance director Nathan Bostock were among those regarded as in the race for succession. The name of Standard Charter's finance director Richard Meddings was also being circulated after Sky News reported last month he was on a list of names recently handed to RBS's non-executive directors.
Hester, who said he would go on holiday once he left the bank, admitted he wanted to stay on to see through a job that many thought might have been completed by now if the economy had recovered more quickly after the banking crisis.
Hester said: "Of course I'd like to have stayed as I feel I've been in the trenches with all of my people helping RBS to recover and privatisation would have been a fitting end to those endeavours."
February: RBS announces the biggest loss in British corporate history – more than £24bn – as Hester admits the taxpayer could end up owning 95% of the bank if its losses continue to mount.
February: Waives £1.6m bonus after coming under pressure from ministers over his pay. Lord Mandelson says Hester was "a rather strong and rather able man whose performance in delivery has not yet been tested."
May: RBS makes £850m provision for mis-selling payment protection insurance. The figure has now risen to more than £2bn.
January: Gives up £1m bonus, bowing to an intense media and political campaign.
February: Says he has been put in charge of "defusing a ticking timebomb" at RBS.
October: RBS leaves the asset protection scheme, a state-backed initiative insuring toxic assets.
February: RBS fined £390m for rigging Libor interest rate – some of the wrongdoing took place on Hester's watch.
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