Cosslett joined IHG from Cadbury Schweppes where he spent 14 years in marketing and general management and was chief executive at IHG from February 2005.
IHG chairman David Webster said: "Andy has been an outstanding chief executive since joining the company in February 2005 and we are very appreciative of the contribution he has made during his time at IHG.
"While we understand and respect his decision to leave at this stage, we are extremely sorry to see him go. Richard and Andy have worked very closely over the last six years and in making this appointment the board is ensuring continuity in management and in our strategy to drive growth."
Although Cosslett has not revealed his plans for the future after leaving IHG, he said the "prospects for the Group are excellent and with IHG entering the next phase of its development, and after six years, this is the right time to hand over the reins".
IHG is now actively looking for a replacement chief financial officer to take up Solomons' post.
Solomons said: "It has been great working with Andy over the last six years. His outstanding leadership has placed IHG in a terrific position. We have an industry leading development pipeline and will continue to build on our success by harnessing the quality of our people, the loyalty of our owners and the strength of our brands. We can look to the future with great confidence."