Whitbread, which earlier this year planned to demerge Costa and list it as a separate entity, said that a sale of the business is now “in the best interests of shareholders”.
Proceeds of the sale will be used to pay down debt and boost the pension fund.
A significant majority of net cash proceeds intended to be returned to shareholders, Whitbread added.
Whitbread will now focus on its Premier Inn hotel chain.
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 international growth potential and accelerates the realisation of value for shareholders in cash.
“This combination will ensure new product development, continued growth in the UK and more rapid expansion overseas.”