The deal, expected to complete in the first half of 2019, plugs a big hole in Coca-Cola's portfolio.
The coffee shop to hotels group said earlier this year that it would split Costa and list it as a separate entity, following pressure from activist investor Elliott.
Whitbread said in a statement on Friday that the deal, which will give Coke nearly 4,000 coffee outlets in the United Kingdom and across Europe, had been agreed unanimously by the Whitbread board as in the best interests of shareholders. The Atlanta-based company is entering the coffee-shop market to make up for waning soft-drink demand, even as competitors such as Starbucks Corp. and JAB have already cornered many key locations. Since then, Costa has grown from just 39 shops to become the biggest coffee firm in Britain.
Coca-Cola plans to use its existing infrastructure to expand Costa's business lines, which include retail outlets, vending machines and coffee for use at home.
"Hot beverages is one of the few remaining segments of the total beverage landscape where Coca-Cola does not have a global brand", said James Quincey, Coca-Cola President & CEO.
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Costa, which doesn't now have a presence in North or South America, was the third-largest coffee shop chain globally in 2017, according to market research provider Euromonitor International, just behind McDonald's McCafe outlets but well behind Starbucks.
Costa doesn't now have a presence in North or South America, but Quincey indicated that one potential early expansion route would be to use Costa's vending operation and grow the company's ready-to-drink products.
"However, the growth story needs to be looked at because Whitbread has chose to change tack, shifting away from a demerger that it said would let the coffee and hotel chains grow more rapidly in favour of a quick sale".
"Coca-Cola are one of the few companies in the world that could justify the valuation", said Nicholas Hyett, equity analyst at Hargreaves Lansdown.
A significant majority of net cash proceeds meant to be returned to shareholders, Whitbread added. Whitbread has stated that the sale of Costa Coffee will allow them to boost the company's pension fund, pay down some debt and expand the Premier Inn chain.
Whitbread's share price soared 14 percent.