Whitbread will now focus on its Premier Inn hotel chain.
Whitbread acquired the chain in 1995, for £19 million when it had only 39 shops. It is now present on most British high streets, with 2,422 outlets across the country and a further 1,399 in worldwide markets, operated as franchises, joint ventures and wholesale outlets.
Whitbread shares climbed more than 16 percent Friday on the London Stock Exchange.
Proceeds of the deal will be used to pay down debt and boost the pension fund.
"It's been a very fast transaction", she said. As of April, Whitbread was planning to slowly spin off Costa.
Whitbread had been under pressure to consider a break-up of the business after hedge fund Elliott Advisors became the company's largest shareholder.
The plan was to complete the demerger by 2020.
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. In China, for example, Mintel has predicted that the coffee market would surge by almost 40% to be worth RMB102bn (£11.5bn; $14.9bn) by 2022.
The Atlanta-based beverage giant described the proposed deal as a necessary entryway to the global coffee market. Over the years, it has owned well-known brands such as TGI Fridays, Pizza Hut and Marriott Hotels. According to reports, the deal will be finalised in the first half of 2019. The spin-off would have taken up to two years, the company had said.
"Coffee culture is also evolving rapidly in wider Asia and is one of the main reasons that Nestlé recently bought the rights to sell a range of Starbucks brands, added Forsyth". The deal also offers Coca-Cola an expanded retail footprint in Europe and China.
"Coca-Cola are one of the few companies in the world that could justify the valuation", said Nicholas Hyett, equity analyst at Hargreaves Lansdown.
The Press Association reported in May that Whitbread had been approached informally over a potential buyout of Costa.