RBS shares dropped 5.9 percent on Thursday morning, after declining as much as 8 percent at one point during the first hour of trade.
Hester's departure after five years at the helm is said to be by "mutual agreement", but the move has rattled shareholders and a source close to the bank said there were internal divisions between Hester and chairman, Sir Philip Hampton.
(Read More: RBS CEO Hester to Step Down This Year )
"What has happened is plain stupid, badly organized and damaging for RBS," one big shareholder told CNBC.
A senior executive close to the bank said there was a "clear split in the way Stephen and Philip saw the bank." Hester was in favor of a bank with an international business, with "a number of business lines in a number of geographies," whereas Hammond's view was the bank needed to be "smaller and U.K. based."
RBS also announced plans to exit all structured retail investor products and equity derivatives to focus on core fixed income. The bank said the move will result in job losses, with Reuters reporting that as many as 2,000 employees will be let go.
Hester has been credited for restructuring the bank and shrinking its balance sheet after the 2008 financial crisis.
(Read More: UK Banks Return to Favor in Turnaround Year )
Speaking to CNBC, RBS Chairman Sir Philip Hampton said board succession has been discussed with the U.K. Treasury and denied that there had been a falling out between CEO Hester and George Osborne, the Chancellor of the Exchequer (finance minister).
"He has many years behind him and arguably not so many ahead of him - in typical CEO span," Hampton said of the reason why the bank and Hester decided to part ways.
James Barty, head of financial policy at the think tank Policy Exchange said Hester had taken on "the toughest job in the U.K."
"He has turned its fortunes around to such an extent that the time is now right for the government to dispose of its shareholding."
In a statement RBS said an "orderly succession" would allow the new CEO to oversee the re-privatization of the bank, and lead it "in the years that follow."
It said Hester "was unable to make that open-ended commitment."
In a video statement released by RBS, Hester expressed mixed feelings about his departure.
"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 privatization would have been a fitting end to those endeavors," he said.
"But it has been a very bruising and difficult job so I certainly don't have to be prised away reluctantly."