Alison Reed will leave the company at the end of April.
M&S chief executive Stuart Rose said Dyson's experience in a company undergoing huge business change will come in handy.
He said: 'Ian [Dyson] comes from a highly competitive sector, which has seen enormous change in recent years. His experience in restructuring businesses will be important in rebuilding the fortunes of Marks & Spencer.'
Rose also thanked Reed for her contribution to the retailer over the past 20 years and conveyed the board's best wishes to her for the future.
The Rank Group owns a mixture of leisure-related companies, including Mecca Bingo and the Hard Rock Café chain.