WASHINGTON -- Almost 4 million homeowners might receive cash compensation and mortgage relief in a multi-billion-dollar settlement with 10 major banks, government regulators announced Monday.

Bank of America, JPMorgan Chase, Wells Fargo and seven other mortgage-servicing companies have agreed to give borrowers $3.3 billion in direct payments and $5.2 billion in the form of loan modifications and other assistance to settle allegations that they wrongly foreclosed on homeowners in 2009 and 2010. The other lenders are Citibank, MetLife Bank, PNC, Sovereign, SunTrust, U.S. Bank and Aurora.

Eligible homeowners may receive payments that range from hundreds of dollars to $125,000, depending on the type of error.

The settlement amounts to a mea culpa by mortgage servicers, who are effectively bill collectors for investors who collectively own mortgages that have been pooled together, often by Wall Street firms, into complex bonds called mortgage-backed securities.

Many servicers were first set up by Wall Street banks, such as Bear Stearns and Lehman Brothers, that disappeared or collapsed during the U.S. financial crisis in 2008. Wall Street banks infamously looked past poor underwriting, particularly in boom states such as Florida and California, because the buck was passed to unsuspecting investors, who thought they were buying AAA-rated mortgage bonds, prompting the slogan, “A rolling loan gathers no loss.”

However, as more and more borrowers failed to meet their mortgage commitments or saw their home values plunge, a housing crisis gained steam in 2008 and 2009. Servicers were overwhelmed with requests for loan modifications, and the problem of homes that now are worth less than the mortgages they carry continues to bedevil the housing market.

The agreement announced Monday ends an “independent foreclosure review” of 4 million loan files mandated in a 2011 enforcement action by the Office of the Comptroller of the Currency and the Federal Reserve. The costly and time-consuming process required banks to hire independent consultants to review the files on a case-by-case basis to identify mistakes such as lost paperwork, miscalculated payments, illegal fees and other slipshod mortgage servicing and foreclosure practices.

The Government Accountability Office reported in July that the review was too complex and borrowers “might not be motivated to participate.”

Regulators said the settlement announcement Monday would provide more speedy relief to borrowers, who now will receive compensation regardless of whether they’ve filed requests for review.

Bank officials said they were pleased to have the independent foreclosure review behind them.

“We have helped nearly 1 million homeowners avoid foreclosure over the last four years and will continue to help others who may be struggling to make their payments,” JPMorgan Chase spokeswoman Amy Bonitatibus said.

Consumer advocates welcomed the decision to replace the failed review process with a settlement that will return at least some cash to victims of unfair banking practices. But they said many problems remained.

“The money is grossly inadequate for homeowners, and the program will require careful oversight to ensure that all homeowners harmed get a fair chance at benefits,” said Ed Mierzwinski, the consumer program director for U.S. PIRG, a nonprofit advocacy group.