Investors, lead by activists Paul Singer's Elliott and USA -based Sachem Head, have been pressuring the British company to split itself up to help unlock value.
"[The Board] believes that it is in the best long-term interests of Whitbread's many stakeholders to separate Premier Inn and Costa, via a demerger of Costa", says Alison Brittain, chief executive of Whitbread.
The company said it had developed Costa into the UK's clear leader in the out-of-home coffee market, and had made improvements in product innovation and digital capability.
Morgan Stanley analysts said the demerger could trigger takeover interest in Costa, which they valued at about 2.6 billion pounds.
He added, "The team will now also be focused on ensuring the demerger of Costa is conducted as fast as practical and appropriate to optimise value for Whitbread's shareholders". Brittain said the decision to make the split was not due to shareholder pressure.
A source familiar with Elliott's plans called the 24-month timeline "extreme".
Costa Coffee shop in Sutton High Street, London.
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The demerger of Costa, which has more than 2,400 United Kingdom coffee shops and around 1,400 outlets overseas, will be completed within two years.
Since taking the helm in 2015, CEO Brittain has driven Costa's expansion in China, a market where Costa's only larger rival Starbucks is planning to more than triple its over 3,000-store network within a decade.
Over the next two years Whitbread will focus on upgrading its IT systems, delivering its efficiency programme, further developing its brands overseas and managing its pension deficit. Whitbread's shares jumped two weeks ago in an indication that the wider market would support the move.
Costa will become a listed entity in its own right will benefit from growth expected in China and Costa Express.
Whitbread has announced that Costa Coffee will be spun off as a separate company, according to Reuters.
Costa's like-for-like sales in its British stores slipped 0.3 percent in the final quarter of the year, it said on Wednesday.
The coffee chain's United Kingdom operating profits were down 2pc at £151m as it battled against rising costs, but it benefitted from soaring sales through its Costa Express vending machines, which churned out £210m of revenue.