NEW YORK — Burger King Holdings Inc. shares jumped nearly 25 percent Thursday, rallying as the fast-food giant said it will be gobbled up by investment firm 3G Capital for $24 a share in a deal valued at $4 billion.

The buyout represents a 46 percent premium to the shares’ price before media reports Wednesday that a deal was in the works, the Miami-based company noted. The transaction is expected to close in the fourth quarter.

TPG Capital LP, Goldman Sachs Capital Partners and Bain Capital Investors own about 31 percent of Burger King between them, and all have agreed to tender their shares.

“”We look forward to partnering with 3G Capital, whose proven track record as an investor, together with its financial and consumer brands experience, will serve to further strengthen the company, our restaurants and franchisees worldwide,”” John Chidsey, the chief executive, said in a news release.

Burger King, founded in 1953, isn’t new to private-equity takeovers. In 2002, beverages giant Diageo sold the No. 2 U.S. fast-food company to TPG, Goldman Sachs and Bain.

Grand Metropolitan PLC, Diageo’s predecessor company, acquired it when it bought Pillsbury, now part of General Mills, which had owned the chain since 1967.

It went public in 2006.

The company has been struggling a bit in the face of high unemployment and the general economic malaise.

Last week, it reported a fourth-quarter profit that fell to $49 million, or 36 cents a share, from $58.9 million, or 43 cents a share, in the final three months of fiscal 2009. Total revenue declined to $623 million from $629.9 million, while same-store sales — those at outlets open at least a year — were off 0.7 percent.

“”We would view this as an excellent opportunity for investors who have been in the shares to cut their losses (or take some modest gains, depending on when shares were bought),”” wrote Mark Kalinowski of Janney Capital, following the first rumors of a sale. “”Burger King may actually be better off as a privately held entity at this point in its history.””

The company “”faces some large, longstanding challenges that may be better solved out of the public eye,”” he added. “”One big challenge is the parent company’s strained relations with its franchisees. Another challenge facing Burger King is: How does it best position itself so that it doesn’t come off to fast-food fans as simply another McDonald’s?””

The news also helped boost shares of Wendy’s/Arby’s Group, which has been the subject of occasional buyout rumors, by about 7 percent.