The mortgage settlement resolves claims brought against the London-based bank by the Justice Department, the Consumer Financial Protection Bureau, the Department of Housing and Urban Development, and 49 states plus the District of Columbia.

The Justice Department said the deal will provide for $370 million in various forms of consumer relief, such as reducing the principal on some borrower's mortgages.

Another $100 million, meanwhile, will be divided up into several pots, with $40.5 million going to the federal government, $59.3 million going into an account that the states will use to pay borrowers who lost their homes in foreclosure, and an additional $200,000 to reimburse state attorneys general for investigative costs.

“We are pleased to have reached this settlement and believe it is a positive result that benefits American homeowners and the US housing industry,” said Kathy Madison, the chief executive officer of HSBC Finance Corp.

She added the bank has worked to "stay focussed on home preservation" and make foreclosure "a last resort option."

The HSBC accord largely mirrors a 2012 national mortgage settlement that federal and state officials struck with five of the country's largest banks, including Bank of America and JPMorgan Chase & Co.

The national mortgage settlement came in the aftermath of the 2007-2009 housing crisis, when many people lost their homes to foreclosure.

The mortgage servicing investigation started after evidence emerged late in 2010 that banks had robo-signed thousands of foreclosure documents without properly reviewing paperwork.

The HSBC agreement requires the company to provide various types of relief to mortgage holders, such as principal reductions and refinancing for underwater mortgages.

HSBC also needs to undertake certain corrective actions.

For instance, it must not foreclose on homeowners being considered for a loan modification and must give those people a chance to appeal denials.

HSBC must also install an independent monitor to review compliance with the settlement, which will be entered into a Washington, D.C. federal court.

“There has to be one set of rules for everyone, no matter how rich or how powerful, and that includes lenders who engage in abusive business practices,” New York Attorney General Eric Schneiderman said in a statement.

By Sarah N. Lynch