Snook (pictured) said: 'When I became chairman of Carphone Warehouse I undertook to do the job for two years. It will be three years this May and it is time to do new things. I will leave knowing that the business has all the strength of board management and market position to continue its momentum.'
At the same time as chairmanship is transferred, chief operating officer David Goldie will be appointed as an executive director to the board.
Snook made his name in the UK as founding chief executive of Orange. Under his management, the mobile phone operator went public in 1996. Snook stepped down from the group at the end of 2001 and joined Carphone in May 2002.
Gildersleeve was a Tesco director for 20 years until last year. He is chairman of Gallaher Group and deputy chairman of EMI Group. He has also served on the boards of Vodafone and Lloyds TSB.