The price is 16 times this year's earnings before interest, taxes, depreciation and amortisation.
Paying about 1 billion pounds more than some analysts had expected, Coke will use its distribution network to supercharge Costa's expansion as it chases current coffee chain market leader Starbucks (SBUX.O) and its nearly 29,000 stores across 77 markets.
Makers of soft drinks are branching out as consumers seek alternatives to sugary sodas. Earlier this month, PepsiCo Inc. agreed to pay $3.2 billion for SodaStream Ltd., which makes carbonated-water dispensers.
This is Coca-Cola's biggest push into operating stores, just as a series of United Kingdom retailers such as BHS go out of business.
Whitbread shares rose as much as 19 percent.
However, shareholders had been pushing for Whitbread to sell or spin off Costa so it could concentrate on its hotel and restaurant business.
However, the proposed sale has to get the approval of Whithead's shareholders, as well as permission from anti-trust watchdogs, the firm said.
The company said that "a significant majority" of the...
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Still, Costa outranks Starbucks in the United Kingdom - it also operates a business of 8,000 self-service machines - and is expanding in markets such as China.
The surprise announcement immediately prompted speculation that the FTSE 100 leisure group's remaining Premier Inn business could also attract the attention of suitors amid growing consolidation in the hotel sector.
Coca-Cola is hoping for a caffeine-fueled boost with the acquisition of British coffee chain Costa.
Coca-Cola's purchase adds to its Georgia coffee brand in Japan and the U.S. group's coffee products in other countries.
Whitbread acquired Costa in 1995 for £19m when it had 39 shops.
Asked if Whitbread had been pressured to accelerate the sale by activist investor Elliott and other hedge funds, Chief Executive Alison Britain said no.
Chief executive Alison Brittain said: "This transaction is great news for shareholders as it recognises the strategic value we have developed in the Costa brand and its global growth potential and accelerates the realisation of value for shareholders in cash".
Rothschild advised Coke on the deal while Goldman Sachs, Morgan Stanley and Deutsche Bank advised Whitbread.