Kaye, who worked for Dixons Retail for more than five years, has left his job less than two months after the £3.9bn merger between it and Carphone Warehouse.
Dixons Carphone confirmed Kaye’s departure last night and welcomed McGregor to the team.
McGregor joins the business from Activision, where he was vice-president of European marketing and shared services.
He was previously international consumer marketing director for the game developer Electronic Arts and, before that, a board account director at Publicis.
McGregor has also served a seven-year stint as a platoon commander in the Army.
A spokesman for Dixons Carphone said: "We are pleased to confirm Ian McGregor has joined Dixons Carphone as marketing communications director. Ian will have responsibility for the advertising creative, media buying, visual store comms and consumer PR of the company's Currys PC World brand."
Dixons Carphone came in for widespread criticism from other marketing professionals over its new brand identity following the August merger,
One critic, labelled the logo "abysmal" and said it looked like that of "a health insurance company for retirees"