Burger King has been sold to 3G Capital, a private equity firm backed by three of Brazil's best-known businessmen, in a deal worth $4bn (£2.6bn).

The $24-a-share agreement is 46% more than Burger King shares closed at on 31 August, the day before rumours of a deal surfaced and sent the shares soaring by 15%.

In a letter to franchisees, who run 90% of the company's restaurants, 3G's managing director, Alex Behring, said: "We share a common goal to improve the Burger King brand experience for guests at both company-owned and franchisee restaurants, while running a sustainable business on an ongoing basis."

3G declined to say if any job losses are planned, either in the UK, where the company has 500 restaurants, or across the group as a whole. However, market watchers said that the new owners would be likely to focus on increasing the proportion of franchised restaurants by "re-franchising" company-owned outlets and expanding in areas such as Asia and Latin America, where the new owners have especially strong links.

David Palmer, an analyst at investment bank UBS, said: "We do not believe a private equity buyout would necessarily foreshadow a significant change in strategy for BK. The company's recently announced refranchising initiative is one we believe a private equity sponsor would support. In our view, improved restaurant assets will be a key to stabilising sales – and this is something that could take several years and require significant reinvestment in assets."

The takeover has been funded by debt, which sources put at $2.8bn, raised from JP Morgan Chase and Barclays. Analysts at stockbrokers Robert W Baird commented: "We would find this level of leverage surprising, given the apparent need for BK to invest capital in initiatives to position the brand for long-term success."

The deal also comes at a particularly challenging time for the fast food chain, which last week said worldwide sales this year were down 2.3%, compared with an increase of 1.2% last year. Sales in North America were down 3.9%. Bitter rival McDonald's saw global sales in the second quarter rise 4.8%, with US sales up 3.7%.

BK's chairman and chief executive, John Chidsey, will stay in his role during a transition period before becoming co-chairman with Behring.

The deal represents the second time the 55-year-old chain has been owned by buyout specialists after it was spun out of then owner Diageo in 2002 by Texas Pacific, Bain Capital and Goldman Sachs in a $1.5bn deal (worth £950m at the time). The private equity groups implemented an aggressive turnaround strategy for the loss-making company, and focused on expanding into emerging markets such as China, Brazil and Russia. They floated the company four years later but retained just under a third of the shares.

The deal also marks another example of Brazil's increasing power as a corporate player. Behring is the right-hand man of fellow Brazilian Jorge Paulo Lemann, having previously worked at the buyout firm the 71-year-old billionaire founded. Lemann, who backs 3G along with Marcel Telles and Carlos Sicupira, are known as "the trio" and are best remembered for building the Brazilian brewery InBev, which in 2008 bought Anheuser-Busch, the maker of Budweiser.

Under the terms of the agreement, Burger King can solicit superior bids until 12 October.