Warren Buffett’s bet on Bank of America Corp. is about to pay off with a roughly $12-billion windfall.

The billionaire plans to exercise warrants obtained six years ago in a vote of confidence in Bank of America while its shares were tumbling amid multibillion-dollar probes tied to the housing meltdown. The cash infusion helped the bank put to rest doubts about whether it had enough capital, and its shares have more than tripled since then.

In the 2011 deal, Buffett’s Berkshire Hathaway Inc. invested $5 billion in Bank of America in exchange for preferred stock and the right to buy 700 million common shares, a stake now worth $17 billion. Berkshire said in a statement Friday that it would convert its preferred shares into common stock once the Charlotte, North Carolina-based bank increases its dividend, now planned for the beginning of the third quarter.

Buffett laid out his thinking for the conversion, which will make him the company’s biggest shareholder, in a February letter to investors, saying that the decision would come down to simple math: The preferred investment pays $300 million a year in dividends, so it makes sense to convert that into common stock if those shares began earning more.

After receiving Federal Reserve approval of its capital plan, Bank of America said on June 28 that it planned to boost its dividend 60 percent to 12 cents a quarter. By converting the preferred stake into common shares, Berkshire’s payout will rise to $336 million a year. The $12 billion in gains come on top of more than $1.5 billion in dividends from the preferred stake over the past six years.

Buffett shored up confidence in Bank of America and its chief executive officer, Brian Moynihan, at a critical juncture. With backing from Berkshire’s billionaire chief executive officer, Bank of America soon rebounded. That generated a massive paper profit on the warrants. The warrants allow Buffett to buy the stock at a discounted rate of $7.14 a share, compared with the closing price of $24.32 on Thursday.

The episode highlighted Buffett’s role as a financial firefighter and mirrored confidence-boosting investments he made in Goldman Sachs Group Inc. and General Electric Co. during the 2008 crisis. In those cases, he was also able to extract generous terms in exchange for vouching for those companies’ long-term prospects.