Sir Fred had been under pressure after the drop in the bank's share price.
He is to be replaced by Stephen Hester, currently chief executive of British Land.
RBS chairman Sir Tom McKillop is also to step down next April.
The move to raise more capital is expected to leave the Government owning around 60% of the bank and give it the power to appoint three board members.
It will also mean that the board members will receive no bonuses in 2008.
Under the scheme, which will be known as the Reconstruction Fund, RBS is to raise £20bn through a Government-guaranteed £15bn share issue and a £5bn Government cash injection.
"We regret having to raise new capital but we believe that decisive action is necessary in these unprecedented market conditions," Sir Tomsaid.
RBS to get £20bn from taxpayers
The departure of Sir Fred came after he was criticised for pursuing the takeover of the Dutch bank ABN AMRO last year even after the credit crunch problems had become apparent.
Dubbed "Fred the Shred" for his approach to banking, he earned both respect and fear in the City as a leading figure in the financial world.
The 50-year-old, who was appointed chief executive in 2000, acquired the nickname after displaying a habit for buying a bank and stripping it of its costs - in particular staff - to generate bigger profits.
His take-over tendency led one analyst to describe him as a "megalomaniac".
Sir Fred's business efforts, which included buying rival NatWest, were rewarded financially.
Last year the law graduate and chartered accountant was paid £4.2m, including a £2.86m bonus.
He has an £8.37m pension pot that will pay him £579,000 a year.
His position had been under scrutiny since the RBS group was forced to raise £12bn from investors earlier this year.
RBS has also written off nearly £6bn from credit crunch-linked investments this year, making it one of the worst UK banks to be affected by the sub-prime loans crisis.
::Meanwhile, Halifax Bank Of Scotland will raise £11.5bn of additional capital, including £3bn through preference shares with the UK Government.
HBOS is being taken over by Lloyds TSB and on completion of the deal, the HBOS chief executive Andy Hornby and chairman Dennis Stevenson will step down.