Warren Buffett’s firm is on track to become the biggest shareholder in Bank of America Corp.

The Charlotte, N.C., bank, the second largest in the country by assets, received permission from the Federal Reserve Wednesday to boost its per-share dividend to 48 cents a year. Mr. Buffett has said a dividend of this size would prompt his Berkshire Hathaway Inc. to swap its preferred shares in the bank into about $17 billion worth of common stock.

The...