The US Justice Department yesterday charged the bank with failing to maintain an effective programme against money laundering and conduct due diligence on certain accounts.
It also charged the bank with violating sanctions laws by doing business with Iran, Libya, Sudan, Burma and Cuba.
HSBC Holdings Plc admitted to a breakdown of controls and apologised for its conduct.
"We accept responsibility for our past mistakes. We have said we are profoundly sorry for them, and we do so again. The HSBC of today is a fundamentally different organisation from the one that made those mistakes," said chief executive Stuart Gulliver. "Over the last two years, under new senior leadership, we have been taking concrete steps to put right what went wrong and to participate actively with government authorities in bringing to light and addressing these matters."
The bank agreed to forfeit $1.256bn and retain a compliance monitor to resolve the charges through a deferred-prosecution agreement.
The settlement offers new information about failures at HSBC to police transactions linked to Mexico, details of which were reported this summer in a US Senate probe.
The Senate panel alleged that HSBC failed to maintain controls designed to prevent money laundering by drug cartels, terrorists and tax cheats, when acting as a financier to clients routing funds from places including Mexico, Iran and Syria. The bank was unable to properly monitor $15bn (£9bn) in bulk cash transactions between mid-2006 and mid-2009, and had inadequate staffing and high turnover in its compliance units, the Senate panel's July report said.
HSBC said it expected to also reach a settlement with British watchdog the Financial Services Authority. The FSA declined to comment.
HSBC's settlement also includes agreements or consent orders with the Manhattan district attorney, the Federal Reserve and three US Treasury Department units: the Office of Foreign Assets Control, the Comptroller of the Currency and the Financial Crimes Enforcement Network.
HSBC said it would continue to co-operate fully with regulatory and law enforcement authorities, and take further action to strengthen its compliance policies and procedures.
US prosecutors have agreed to defer or forego prosecution.
It is the third time in a decade that HSBC has been penalised for lax controls and ordered by US authorities to better monitor suspicious transactions.