HONG KONG — McDonald’s said on Monday that it would sell its businesses in mainland China and Hong Kong for $2.08 billion to Citic, a state-owned conglomerate, and the Carlyle Group, a private equity firm.

The deal gives Citic and Carlyle franchise rights for 20 years. Citic and its investment arm, Citic Capital, will have a controlling stake of 52 percent, while Carlyle will take 28 percent. McDonald’s will retain the remaining fifth of the company.

“China and Hong Kong represent an enormous growth opportunity for McDonald’s,” Steve Easterbrook, McDonald’s chief executive, said in a news release. “This new partnership will combine one of the world’s most powerful brands and our unparalleled quality standards with partners who have an unmatched understanding of the local markets.”

Mr. Easterbrook, who took over in 2015 and set about turning the company around, has seen it regain its financial footing recently, although growth has slowed.