The news was announced by his business partner Richard Beatty, with whom Mr Norman co-founded the popular London restaurants Spuntino and Polpo.
Mr Beatty said: ‘It is with the greatest sadness I announce the loss of my best friend Russell Norman.
‘After a short battle in hospital, he died surrounded by family and friends.
Mr Beatty added: ‘Russell is survived by his wife and three children. I ask that you respect the privacy of his family, friends and colleagues at this time.’
Mr Norman was married to Jules McNally and had three children – two daughters, Martha and Mabel, that he had with Ms McNally, and son Ollie from a previous relationship.
Mr Norman died following a cardiac arrest, London’s Evening Standard newspaper reported.
Tributes have poured in, including from restaurant critic Jay Rayner who hailed Mr Norman was ‘one of the most gifted of restaurateurs’.
He said: ‘So sorry to hear of the death, far too young, of Russell Norman.
‘He was one of the most gifted of restaurateurs, a terrific writer and an awful lot of fun to be around.
‘He very much lived life his own way. My thoughts are with his family and friends.’
Fellow London restauranter Robin Gill said he was ‘totally shocked’ by the passing of Mr Norman, who he said was an ‘legend’ and an ‘inspiration’, the online restaurant guide Square Meal reports.
Mr Norman published several cookbooks, the first of which was called Polpo and sold 250,000 copies and was the Waterstones Book of the Year in the same year.
The restauranter presented a six-part documentary for BBC2 in 2014 called The Restaurant Man.
In 2016, his second book, Spuntino, won the Guild of Food Writers award for the best food and travel book.
His third book, Venice: Four Seasons of Home Cooking, was released in 2018. He said of the experience of writing it that he had ‘exiled’ himself to the most beautiful city in the world to ‘learn to cook like a 90-year-old Venetian granny’, Restaurant Online reported.
Read More: Russell Norman: Tributes pour in after BBC star and restaurateur once hailed the ‘king of Soho dining’ for inventing concept of Italian small plates and reviving the Negroni dies aged 57 following ‘cardiac arrest’