The move comes less than a week after the bank was fined for trying to manipulate inter-bank lending rates, sparking a government inquiry and calls for criminal investigations.

Mr Diamond said he was stepping down because the external pressure on the bank risked "damaging the franchise".

BBC business editor Robert Peston said the Barclays boss was encouraged to go by the Bank of England and the FSA.

"They were unable to force him out," our correspondent says, "because the recent FSA investigation into how Barclays attempted to rig the important Libor interest rates did not find him personally culpable."

"However, as a regulated institution, it was impossible for Barclays' board to ignore the revealed wishes of the two most powerful regulators in the City."

Earlier, Lord Turner, the chairman of the Financial Services Authority, described the outrage that has built up over the bank's actions.

"The cynical greed of traders asking their colleagues to falsify their Libor submissions so that they could make bigger profits - has justifiably shocked and angered people, in particular when we are facing hard economic times provoked by the financial crisis," he told the Financial Services Authority's annual meeting.

Barclays chairman Marcus Agius, who had announced his own resignation on Monday, will now take over the running of Barclays until a new chief executive is appointed.

The bank refused to comment on reports that chief operating officer Jerry del Missier, one of the executives to give up his bonus after Barclays received a record fine for Libor manipulation last week, was also planning to step down.

Mr Diamond will still appear before MPs on the Treasury Committee on Wednesday to answer questions about the Libor affair.

"I look forward to fulfilling my obligation to contribute to the Treasury Committee's enquiries related to the settlements that Barclays announced last week without my leadership in question," Mr Diamond said in a statement.

"It is the right decision for the country," Mr Osborne said, saying the UK needed a strong Barclays concentrating on lending and contributing to economic recovery.

Labour leader Ed Miliband said it was "necessary and right" that Bob Diamond stepped down.

"But this is about much more than one individual, it's about the culture and practices of the banking industry," he said.

"That's why we need a full, judge-led, independent inquiry, to get to the bottom of those practices and make recommendations for change in the future. We've had missed opportunities before, we've got to seize this moment."

Labour is critical of the government's decision to call a parliamentary inquiry, chaired by the head of the Treasury Committee, Andrew Tyrie MP, rather than a full Leveson-style inquiry, independent of politicians.

Last week, regulators in the US and UK fined Barclays £290m ($450m) for attempting to rig Libor and Euribor, the interest rates at which banks lend to each other, which underpin trillions of pounds worth of financial transactions.

Staff did this over a number of years, trying to raise them for profit and then, during the financial crisis, lowering them to hide the level to which Barclays was under financial stress.

Mr Diamond is one of the UK's highest paid chief executives, earning £20m last year, and was described as "the unacceptable face" of banking by the then business secretary Lord Mandelson in 2010.

The details of any severance package are not yet known, but former City minister Lord Myners suggests it could add up to £20m-£30m.

"I think his resignation letter is drafted with an eye to that [pay-off], because he admits no guilt on his part at all," the Labour peer told BBC News.

"The shareholders of Barclays will be expecting the board to ensure that not a penny more is paid to Bob Diamond than that to which he is legally entitled," he said.

US-born Mr Diamond was head of Barclays Capital, its investment bank division, when its staff were trying to manipulate the key inter-bank rates.

"He maintains that he didn't know what was going on," says Robert Peston.

It emerged over the weekend that Mr Diamond spoke to the deputy governor of the Bank of England Paul Tucker about Barclays' Libor submissions at the height of the credit crunch in 2008.

The details of that telephone conversation will be an important area of questioning at this week's hearing of the Treasury Committee.

Barclays' managers came to believe, after the conversation between Mr Diamond and Mr Tucker, that the Bank of England had sanctioned them to lie about what they were paying to borrow when providing data to the committees that set the Libor rate.

Investigations are continuing in the UK and the US into other banks over Libor fixing, including criminal investigations by the Department of Justice. The Serious Fraud Office in the UK is looking into possible criminal prosecutions.