Vandevelde will remain the French supermarket giant's chairman, but will no longer represent the Halley family, which owns 13 per cent of Carrefour's capital and 20 per cent of its voting rights.
Vandevelde has been replaced by Bernard Bontoux as chairman of its holding company.
It is understood that Vandevelde stepped down as the Halle family's representative last month, having served for a decade. Vandevelde was appointed Carrefour chairman in 2005.
Separately, it was disclosed that Vandevelde had recently bought almost E10 million (£6.66 million) of Carrefour's stock fuelling speculation that a bid may be launched to buy the retailer.
Vandevele was appointed M&S chairman in 2000 and left in 2004. During his tenure at M&S, the retailer continued to lose market share.