LONDON — British American Tobacco said on Tuesday that its sweetened offer to buy the stake in Reynolds American that it did not already own had been accepted, a $49 billion deal that would create a tobacco giant with a significant presence around the world.

The purchase would create the world’s largest publicly traded tobacco business, based on net sales, and it would combine companies with brands that include Camel, Lucky Strike, Newport and Pall Mall. It comes as the industry faces a shift toward so-called next-generation products, or N.G.P.s, such as e-cigarettes and vaping products.

The agreement came nearly three months after British American Tobacco first offered to buy the 57.8 percent of Reynolds American that it did not own, at the time offering about $47 billion.

“It will create a stronger, global tobacco and N.G.P. business with direct access for our products across the most attractive markets in the world,” Nicandro Durante, the British American Tobacco chief executive, said in a news release. “We believe this will drive continued, sustainable profit growth and returns for shareholders long into the future.”