The move follows the resignation of chairman Marcus Agius and comes less than a week after Barclays Bank was fined a record amount for trying to manipulate inter-bank lending rates.
Bob Diamond said he was stepping down because the external pressure on Barclays risked “damaging the franchise”.
British PM David Cameron has described the rigging of Libor rates as “a scandal”.
“I am deeply disappointed that the impression created by the events announced last week about what Barclays and its people stand for could not be further from the truth,” Bob Diamond said in a statement.
He will still appear before MPs on the Treasury Committee to answer questions about the Libor affair on Wednesday.
“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,” Bob Diamond said.
Last week, regulators in the US and UK fined Barclays £290 million ($450 million) 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.
The Serious Fraud Office is also considering whether to bring criminal charges.
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