Trade minister Lord Green, who was chairman of HSBC at the time the bank was accused of facilitating money laundering for drug king pins, rogue states and terrorists, is to step down from the government.
David Cameron, who made the announcement at the start of prime minister's questions on Wednesday, said Lord Green would be replaced by the current chief executive of BT, Ian Livingston.
Last year HSBC apologised after a US Senate investigation accused it of, among other suspect activities, providing services to some lenders in Saudi Arabia and Bangladesh believed to have helped fund al Qaeda and other terrorist groups.
Senator Carl Levin, the chairman of the subcommittee investigating the bank, said the culture of HSBC's non-UK subsidiaries had been "pervasively polluted for a long time" and said senior executives in London "knew what was going on but allowed the deceptive conduct to continue".
At the time the British government said it had "every confidence" in Lord Green's ability to fulfil his ministerial duties.
Ed Miliband used the revelations about the activities of HSBC to justify his demand for a judge-led inquiry into the culture and practices of the banking industry.
In the event a parliamentary commission on banking standards was set up instead. In its report published today it recommended senior bankers be held personally responsible for malpractice - including the prospect of them facing jail.
Following the announcement that Lord Green would be stepping down, Cameron said he supported the idea of reckless bankers being sent to prison and having payment of their bonuses delayed.
He said: "Penalising, including criminal penalties against bankers who behave irresponsibly, I say yes. Also, making sure that banks who are in receipt of taxpayers' money that you can claw back bonuses, I say yes too."