The investigation of Europe (Chicago Options: ^REURUSD - news) 's largest bank has focused on the transfer of billions of dollars on behalf of nations such as Iran and the movement of money through the US financial system from Mexican drug cartels.
The bank is expected to pay $1.25bn (£778m) in forfeiture - the biggest such amount in any case involving a bank - on top of $655m (£408m) in civil penalties.
Under what is known as a deferred prosecution agreement, the bank will be accused of violating the Bank Secrecy Act and the Trading With The Enemy Act.
Following the announcement, Sky's City Editor Mark Kleinman learned that the financial penalty will result in lower bonus payments among top executives .
The bank's chief executive, Stuart Gulliver, said it accepted responsibility for its past mistakes.
"We have said we are profoundly sorry for them, and we do so again," he said in a statement.
"The HSBC of today is a fundamentally different organisation from the one that made those mistakes.
"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 added that it also expected to reach a settlement with the Financial Services Authority in the UK.
A US Senate investigative committee reported earlier this year that in 2007 and 2008, HSBC Mexico sent about $7bn (£4.35bn) in cash to the US. The committee said such an amount of cash pointed to illegal drug proceeds.
The current trade minister, Lord Green, was HSBC's chairman from 2006 to 2010, after serving as its chief executive between 2003 and 2006.
Last month it emerged HSBC had set aside as much as $1.5bn (£935m) to cover the bill from US authorities.
The HSBC agreement comes after another London-based bank, Standard Chartered (Other OTC: SCBFF.PK - news) , agreed to pay $340m (£203m) to settle federal charges that it laundered money on behalf of four countries, including Iran, that were subject to US economic sanctions.
With US officials increasingly cracking down on money laundering by banks, Credit Suisse (NYSEArca: CSMA - news) , Barclays (LSE: BARC.L - news) and Lloyds have all paid settlements since 2009 related to allegations that they moved money for people or companies that were on the US sanctions list.
Before HSBC's fine, the largest amount paid out was by ING Bank NV in June, which agreed to pay $619m (£384.8m) to settle allegations that it violated sanctions against countries including Cuba and Iran.
More From Sky News