With an executive career spanning more than two decades, Mr Crozier had served as chief executive at ITV, the Royal Mail, the Football Association, and Saatchi and Saatchi.
He will replace Richard Baker when he retires as chairman in February. Mr Baker has been on the Whitbread board for almost nine years, serving the past four years as chairman.
Mr Crozier joined the board of Whitbread in April last year as senior independent director. He was also appointed as the chairman of UK-based cinema chain Vue International, in September.
Arguably, one of the most pressing issues facing Adam Crozier will be to address the speculation about whether the company is going to be broken up.
Last week, Crozier said that he supported the strategy set out by chief executive Alison Brittain.
This involves introducing finer blends in its coffee shops to attract new customers, the introduction of more self-service “express machines across the UK, and expanding into new markets such as China.
“We have a very strong management team and an exciting plan to continue to deliver growth in our core UK businesses, while developing our international business through growth in Germany, China and Costa Express,” said Mr Crozier.
Speaking of his departure, Mr Baker said that his stepping down comes as the company enjoys “considerable momentum” and “aligns with a personal intention… to progressively scale back my business responsibilities.”