The French chef, who was famous for opening Le Gavroche with his late brother Michel Roux, had been unwell for some time.
Le Gavroche became the first restaurant in the UK to be awarded a Michelin star.
Roux was also Chef ambassador of The Clink charity Restaurant Group.
The Clink runs restaurants at prisons including Highdown in Sutton in order to give prisoners the chance to train as chefs.