Burger King Holdings has agreed to sell itself to investment firm 3G Capital for $3.26 billion, giving the No.2 US fast-food chain breathing room to fix its business and close the gap with leader McDonald's Corporation.

At $24 per share, the offer represents a 46 per cent premium to Burger King's price before news of the negotiations emerged on Wednesday.

'It was a call out of the blue,' Burger King chairman and chief executive John Chidsey told Reuters in an interview when asked about how the talks started. He declined to give additional details.

Chidsey will keep his roles during a transition period and then become co-chairman with 3G managing director Alex Behring.

The sale, worth about $4 billion including debt, is expected to close in the last three months of 2010. Burger King has until October 12 to solicit a richer offer from other buyers.

'It looks like a good price for Burger King shareholders. I don't anticipate that someone is going to come in higher,' said Telsey Advisory Group analyst Tom Forte.

'The valuation is based on good fundamentals, which Burger King doesn't have and probably won't have for another year,' said Stifel Nicolaus restaurant analyst Steve West. On Wednesday, he had issued a research note saying that a $23-per-share price would satisfy shareholders.

Analysts said the deal's valuation - at almost nine times cash flow over the last year - is higher than previous restaurant deals and could pave the way for more.

TPG Capital, Goldman Sachs Group's Goldman Sachs Capital Partners and Bain Capital Investors collectively own about 31 per cent of Burger King and will tender their shares into 3G's offer, due to begin by September 17.

Burger King's private equity investors took the company public just four years ago at an initial share price of $17.

3G, a little-known investment firm, was last in the spotlight in 2008, when it waged a proxy battle alongside The Children's Investment Fund against US railroad CSX Corp. That led to Behring joining the railroad's board.

3G's backers include Brazil's Jorge Paulo Lemann, who sits on the board at Anheuser-Busch InBev NV. Forbes magazine estimates his fortune at $11 billion.

'This looks to be something of a new line of business for 3G, which has historically held a concentrated portfolio of high-quality publicly traded businesses, rather than buying companies outright,' Bernstein analyst Sara Senatore said.

The deal is the biggest in a string of recent restaurant buyouts. This summer, Carl's Jr parent CKE Restaurants and Brinker International's On the Border Mexican Grill & Cantina were sold to private equity shops.

Wendy's/Arbys in June said an unnamed party had expressed interest in a potential deal involving the fast-food company, while California Pizza Kitchen Inc and Benihana Inc are looking for buyers.

Burger King, which has been hurt by high unemployment rates among its core audience of young men, expects weak demand during its new fiscal year due to the US economy's slow pace of recovery and government austerity programs in Europe.

Analysts said going private would free Burger King to make major changes without the distraction of pleasing Wall Street.

In particular, West said Burger King needs to remodel its restaurants, which he said are older and less appealing than those operating under McDonald's Golden Arches.

Burger King, known as the 'Home of the Whopper,' also needs to upgrade its technology to allow it to track sales trends in real time, analysts said.

McDonald's has muscled a bigger share of the market by expanding its menu with salads and apple dippers - which appeal to moms and kids - and high-profit beverages like lattes, fruit smoothies and frappes.

Telsey's Forte would like to see Burger King's new owners stick with the company's 'barbell' strategy of selling low-priced and high-priced food.

Value-priced menu items, like its previously offered $1 double cheeseburgers, boosted sales but squeezed franchisees.

On the flip side, it has introduced a new broiler system that allows the chain to quickly prepare larger, 'premium' Steakhouse XT burgers that sell for $4 and bone-in ribs, which quickly sold out despite their price of $7 for an eight-piece order. Such items appeal to its young, hungry male clientele, but sales could be constrained by weak economy.

Burger King is rolling out an expanded breakfast menu this autumn and Chidsey said 3G has strong connections internationally, where the chain has opportunities to expand.

Lazard, JPMorgan Securities and Barclays Capital acted as advisers to 3G Capital. Morgan Stanley and Goldman, Sachs & Co advised Burger King.-Reuters