Whitbread acquired Costa in 1995 for £19 million from founders Sergio and Bruno Costa when it had only 39 shops.
Nicholas Hyett, equity analyst at Hargreaves Lansdown, described the deal as "a bitter-sweet moment for Whitbread investors".
The U.S. group's interest in Costa predated the demerger announcement, and the fact that Mr. Quincey, who took charge of Coca-Cola in May previous year, is British would have helped to put the coffee chain on the soft-drinks company's radar, the Whitbread boss added.
Whitbread-owned Costa, which was founded in London in 1971, has grown into a global brand with an established presence in parts of Europe, the Middle East and Africa, as well as a growing footprint in China. JAB Holdings, an investment holding company, has been buying up businesses and brands associated with Peet's, Caribou, Stumptown and Krispy Kreme Doughnuts.
"Whitbread, which also owns budget hotel chain Premier Inn, said that its board had unanimously approved the deal, and that it expects the sale to be completed by the first half of 2019".
The research firm Mintel estimated that the global coffee shops market was worth £127.3bn ($165bn) in 2017, while another £43.2bn ($56bn) worth was sold in shops - whether as beans or the increasingly popular pods used by consumers playing barista at home. Coca-Cola is getting into the coffee business.
Whitbread said it will use the money to reduce its debt, increase its contribution to the pension fund and return a "significant majority" to shareholders.
The Costa deal opens a new business line for a company synonymous with fizzy, sugary beverages like Coca-Cola, Sprite, or Fanta, underscoring the pressure to find new areas of growth as consumer tastes change.
The deal comes hot the heels of another big money acquisition in the sector.
"This transaction is great news for shareholders as it recognizes the strategic value we have developed in the Costa brand and its worldwide growth potential, and accelerates the realization of value for shareholders in cash", she said.
Chief executive Alison Brittain said Whitbread would now focus on its Premier Inn business in the United Kingdom and Germany.
Coca-Cola shares were slightly down Friday in mid-morning trading.