In the lengthy letter he said: "I do recognise that our culture, and that of the industry overall, needs to evolve. The financial crisis revealed that banks need to revisit the basis on which they operate, and how they add value to society."
He added: "I am disappointed because many of these behaviours happened on my watch. It is my responsibility to make sure that it cannot happen again."
Meanwhile, group chairman Marcus Agius confirmed his resignation from the bank's board, after saying that "the buck stops with me".
In his resignation letter he said: "It has been my privilege to serve as Barclays chairman for the past six years.
"This has been a period of unprecedented stress and turmoil for the banking industry in particular and for the wider world economy in general.
"But last week's events- evidencing as they do unacceptable standards of behaviour within the bank have dealt a devastating blow to Barclays' reputation.
"As chairman I am the ultimate guardian of the bank's reputation. Accordingly the buck stops with me and I must acknowledge responsibility by standing aside."
Mr Agius has also announced that he is to step down as chairman of the British Bankers' Association (BBA).
The development comes after the lender was fined a record £290m by regulators in the United States and Britain over the manipulation of the London interbank lending rate, known as Libor, and its equivalent in Europe (Chicago Options: ^REURUSD - news) - Euribor.
Mr Diamond is expected to disclose allegations partially blaming the Bank of England (BOE), after it emerged he spoke with its deputy governor Paul Tucker in 2008 about the Libor rate.
Barclays' traders were said to have "mistakenly" believed the BOE condoned a rate fix after the discussion, however the BOE has categorically denied anything to do with fiddling the rate – used to help set the rate for mortgages and credit cards.
Labour MP John Mann, who sits on the Treasury Select Committee, said drawing the BOE into the affair would distract focus away from Barclays.
Mr Mann, who has called for Mr Diamond's resignation, said he would ask why he allowed three years of proven interest rate deception and dishonesty, why nobody has been sacked from his staff and why he kept his bonus over the three-year period covered by the Libor-fixing claims.
Mr Agius has been further embroiled in the scandal because of his role as BBA chairman, which is responsible for control of Libor.
The association said in a statement: "The British Bankers’ Association is shocked by the report about Libor.
"The BBA has proactively co-operated with the authorities at every stage and will continue to work with the regulatory investigations into Libor, submitting information and making staff available for interview."
Prime Minister David Cameron told the Commons that a full parliamentary inquiry would be set up in the wake of the Libor scandal.
Barclays said Mr Agius will remain in post until an "orderly succession is assured" and his departure is believed to secure the position of Mr Diamond.
Sky's City editor Mark Kleinman said: "That is because the Financial Services Authority would not allow the simultaneous exit of the chairman and chief executive of a major bank like Barclays."
Amid the chairman's resignation, pressure still remains on Mr Diamond and his alleged role in the Libor scandal.
Conservative peer Baroness Wheatcroft told Sky News: "I don’t think this solves the problem and Marcus Agius should not be carrying the can for Bob Diamond."
Bookmaker William Hill has offered 7/4 odds that Mr Diamond will be pushed from the board by the end of July.
"Ninety-nine per cent of the bets we have taken since opening the book, when Mr Diamond was 11/4 to go, have been for him to depart before the end of this month," William Hill (Other OTC: WIMHF.PK - news) spokesman Graham Sharpe told Sky News Online.
"But if he refuses to quit he may be able to tough it out."
Kleinman said the Barclays board is set to commission an independent inquiry into events at the bank following Mr Agius' resignation.
He said: "Board members are throwing their support behind the idea of a probe of what one shareholder described to me last week as Barclays' 'Wild West culture'."
Baroness Wheatcroft added: "Those within the bank probably have a pretty good idea of what needs to be done.
"They all have got to change the way they behave."
Labour is to table an amendment to the Financial Services Bill in the House of Lords today, calling for a full and public inquiry to restore confidence in the proper functioning of the markets.
The party hopes to raise the matter later in the week when a clause in the bill relating to the new Financial Conduct Authority's responsibility to ensure the proper functioning of the markets is debated in committee.
And a senior Labour source said they hope to force a full parliamentary debate and vote on their calls for an inquiry "at the earliest possible opportunity".