He died on Wednesday night at his home in Berkshire, southeast England, his family confirmed.
“It is with deep sadness that the Roux family announces the passing of our beloved grandfather, father, brother and uncle, Michel Roux OBE. The family would like to thank everyone for their support during his illness,” his children Alain, Francine and Christine said in a statement.
“We are grateful to have shared our lives with this extraordinary man and we’re so proud of all he’s achieved.
“A humble genius, legendary chef, popular author and charismatic teacher, Michel leaves the world reeling in his wake. For many, he was a father figure inspiring all with his insatiable appetite for life and irresistible enthusiasm.
“But above all, we will miss his mischievous sense of fun, his huge, bottomless heart and generosity and kindness that knew no bounds. Michel’s star will shine forever lighting the way for a generation of chefs to follow.”
Born in Burgundy, France, Roux left school at the age of 14 to become a pastry apprentice, his family said, before moving to Britain in 1967.
There he opened the world-famous London restaurant, Le Gavroche, which went on to become the first British restaurant to win three Michelin stars.
In 1972 he opened The Waterside Inn in Bray, Berkshire, which was awarded its third Michelin star in 1985 and is the only restaurant in the world outside France to have retained three stars ever since.
A prolific author, Roux published 15 books, which sold millions of copies worldwide.
In 1982 he and his brother Albert Roux founded the Roux Scholarship, a prestigious cooking competition for chefs that enables them to train in the greatest restaurants in the world.
The Roux Scholarship posted on Instagram that it was “deeply saddened” by his death.
The Michelin Guide said in a tweet
: “Michel Roux OBE was a true titan of the hospitality industry. He inspired a whole generation of chefs and the UK restaurant scene would not be what it is today were it not for his influence.
“Our thoughts are with his family and the many who worked with this legendary chef.”