Barclays executive chairman Marcus Agius, who is being questioned by MPs about the scandal, said Mr Diamond had given up his bonus voluntarily.
Mr Diamond will get up to a year's salary, pension allowance and benefits.
The committee is trying to establish the role the Bank and the government played in the rate-fixing.
Mr Agius, a senior non-executive director on the BBC executive board, also resigned but agreed to stay on to find Mr Diamond's successor.
Mr Diamond has already given evidence to the Treasury Committee.
Last week, he told MPs he had spoken in October 2008 to Mr Tucker, who had expressed concerns about the high level of Libor - the rate at which banks lend to one another and which is the basis for millions of daily financial transactions - being submitted by Barclays.
Mr Diamond's note of the call concluded by saying Mr Tucker had stated that "it did not always need to be the case that we appeared as high [with Libor submissions] as we have recently".
Emails released by the Bank of England also show there was regular contact between Mr Tucker and Mr Diamond, and between Mr Tucker and senior Downing Street official Sir Jeremy Heywood, during the height of the financial crisis.
Later, Barclays lowered its Libor submissions, leading to speculation that it had done so as a a result of pressure from the Bank.
However, on Monday, Mr Tucker told the Treasury Committee that he did not give Barclays instructions to lower its Libor submissions in 2008.