Slipper, who gives up his role next month, has worked for the PC and printer brand for 12 years, having been its top marketer for Europe, the Middle East and Africa since 2002. He is not thought to have another job to go to.
News of his exit comes shortly after a repositioning of the HP brand. Its latest ads, intended to make HP seem more consumer-friendly, use the line 'The computer is personal again'.
HP is currently embroiled in allegations of spying on its board members, which led to the resignation of its chairman, Patricia Dunn, last week.