Dempsey is, in effect, filling the gap caused by the sudden resignation of BBC director general George Entwistle and his replacement by Tony Hall, who will start next March This means that Davie, the current acting director general, will return to head up BBC Worldwide in March 2013
Dempsey will be running BBC's commercial arm from December until March.
John Smith, BBC Worldwide’s current chief executive, last month announced his decision to step down after eight years in charge of the company and will leave the business in December.
The appointment of Dempsey was made by Davie in his capacity as acting director-general.
In his current role, Dempsey oversees Consumer Products, a global producer and distributor of TV entertainment packaged media, including DVD, Blu-ray, DTO, licensed product, music, BBC Shop and book publishing partnerships.
He joined BBC Worldwide in 1998 as UK sales director and became managing director of BBC Audiobooks in 2002. He was appointed director of BBC Worldwide's audio and music business when it was established in 2006.
Prior to joining BBC Worldwide, Dempsey's background in sales and marketing included eight years at Mars Confectionery, followed by two years as sales director of Frontline Ltd, BBC Worldwide's magazine joint venture business.
As a result of the move, Marcus Arthur, managing director for global brands, will take over Dempsey's current responsibilities as acting managing director for consumer products, in addition to his current role.
Dempsey said: "I am proud and privileged to have been asked by Tim to take on these responsibilities as an interim measure until he arrives early next year. BBC Worldwide is a dynamic company with exciting times ahead of it. My immediate priority will be to provide the company with leadership and direction, so it can keep on delivering great returns to the BBC."
Davie said: "Paul has a great track record at BBC Worldwide and a sound understanding of the commercial imperatives that have made it an international success. I have every faith that he is the right person to lead BBC Worldwide over the coming months and make sure it carries on supporting the BBC brand around the world."