He will be replaced by the current head of Whitbread Restaurants Paul Flaum.
Under Dempsey, Premier Inn grew from having 32,600 rooms when the brand was launched in 2007, to 57,000 rooms today.
Whitbread’s chief executive Andy Harrison said: “I would like to thank Patrick for his tremendous contribution to Whitbread over the last decade.
“During this time we have transformed Premier Inn into the UK’s biggest and best hotel chain and developed exciting new growth opportunities with the launch of hub by Premier Inn, and our recently announced entry into the German hotel market.”
Flaum will assume the role of company MD on 1 March 2015 after Dempsey’s departure. Flaum has been at Whitbread for 11 years and was chief operating officer for WHR prior to becoming Restaurants MD.
More internal promotions will see current marketing and strategy director Simon Jones assume the role of MD Premier Inn UK and hub by Premier Inn, and Mark Anderson, the current MD for property, procurement and logistics, will take responsibility for Premier Inn Germany.
Harrison added: “We have very ambitious growth plans which, combined with the strength of our current performance, makes this a good time to implement our succession plans.
“The changes announced today broaden the leadership of WHR, provide more focus on our growth opportunities and bring on the next generation of talent. Whitbread has laid out clear five-year growth milestones and we have the strength and depth of leadership to successfully deliver those goals.”
Dempsey said: “I am enormously proud of my team's achievements with Premier Inn and Whitbread Restaurants.
“With the Premier Inn brand growing so successfully over the last eight years we believe that now is the right time for me to hand over the baton. I am particularly delighted to see so many internal promotions and have every confidence in the new team.”