Whitbread bought the coffee chain in 1995 for $19mn when it had 39 shops. Today it has almost 4,000 shops in 32 countries.
The group said it is selling Costa to focus on its Premier Inn hotel business.
"The Costa team and I are extremely excited to be joining The Coca-Cola Company,” said Costa Managing Director Dominic Paul.
“Costa is a fantastic business with committed and passionate associates, a great track record and enormous global potential.
“Being part of the Coca-Cola system will enable us to grow the business farther and faster."
For Coca-Cola, the expected acquisition gives it a foot into the growing coffee market.
Costa is the second largest coffeehouse chain in the world and the largest in the UK.
“Costa gives Coca-Cola new capabilities and expertise in coffee, and our system can create opportunities to grow the Costa brand worldwide,” said Coca-Cola President and CEO James Quincey.
“Hot beverages is one of the few segments of the total beverage landscape where Coca-Cola does not have a global brand. Costa gives us access to this market with a strong coffee platform.”
Following the announcement, Whitbread shares rose more than 17% in early Friday trading, adding around £1bn (US$1.3bn) to its market value.
The purchase comes shortly after coffee chain Pret A Manger was sold to JAB Holdings for £1.5bn (US$1.95bn) in May.