Bank of America Corp. on Wednesday announced an agreement to pay $8.5 billion to settle claims by a group of high-profile investors who lost money on mortgage-backed securities purchased before the U.S. housing collapse.

The payment would be the largest such settlement by a financial-services firm to date, exceeding the total profits of the Charlotte, N.C., bank since the onset of the financial crisis in 2008. Bank of America's board approved the settlement during a meeting Tuesday to discuss the matter, one of these people...