Gary Leih, the Ogilvy Group UK chairman, will take over as the chief executive until a replacement is found.
Jackson, who has spent most of his career handling major accounts, was made the chief executive in 2002.
His move means Jackson will no longer be given a place on the yet-to-be-established UK management board when Leih instigates the group's restructure later in the year.
The new structure will unite Ogilvy's 11 UK businesses, including OgilvyOne and 141, under a single management team of 16 group partners.
Rory Sutherland, who will sit on the management board, has already been appointed the vice-chairman of Ogilvy Group UK. He will be joined on the management board by OgilvyOne's joint managing directors Mike Dodds and Guy Lambert.
Leih said: "This appointment will see Paul cast in a fully client-facing international role where his talents are already well known."
In his new position, Jackson, who will report to John Seifert, the chairman of Ogilvy's Global Brand Community, will handle all aspects of O&M's American Express account outside North America. The agency handles the business across 30 markets globally.
Jackson said: "Having enjoyed my time in general management at O&M London, I relish the opportunity of returning to a more client-facing role, shepherding one of our biggest and longest-standing relationships."
Jackson rejoined O&M in July 1999 to work on the Ford business across Europe, having previously worked for the agency at the beginning of his career.
Before returning to O&M, his career included spells at Publicis, Bates and Lintas. He was also a founding partner of the integrated agency KMM, which was built around the Rover business.