Cosslett is thought to be leaving of his own volition and will be succeeded by Richard Solomans, the company's current chief financial officer, who will take over on 1 July.
Cosslett is on the executive committee of the World Travel and Tourism Council. He has been chief executive of IHG since February 2005, joining after a 14-year career in marketing and general management at Cadbury Schweppes.
His roles at the company included chairman, Cadbury Schweppes Australia, chief executive of the Asia Pacific confectionary business, managing director, Great Britain and Ireland, and president, EMEA.
Before working for Cadbury Schweppes, Cosslett spent 11 years at Unilever.
Solomans has been chief financial officer and head of commercial development at IHG since 2003.
He has worked for the group since 1992, holding a number of senior roles including chief operating officer, America Hotels division.
Solomans was also chairman and finance director of Britvic, prior to its initial public offering (IPO) in 2006.
Cosslett said: "Richard is a great colleague who has been at the heart of the business since IHG became an independent company in 2003.
"He has intimate knowledge of our hotel operations and brands and enjoys close relationships with our owners and partners around the world. I know IHG will go from strength to strength under his leadership."This week, IHG formed a partnership with Apple to introduce the iPad as part of its concierge service.