Regis won five caps for England between 1982 and 1987, having been one of the stars of the Baggies team between 1977 and 1984.
He scored 112 goals in 297 appearances for Albion before moving on to Coventry, winning the FA Cup with the Sky Blues in 1987.
The Professional Footballers’ Association announced the news on Monday morning and wrote in a tweet from its official account: “A true gentleman and legend, he will be deeply missed. Our sympathies to his family and friends.”
Regis was born in French Guiana in February 1958 but moved to London with his family at the age of five.
He did not come through the youth ranks with a professional club and was instead spotted playing Sunday morning football by the chairman of Surrey non-league club Molesey.
West Brom signed him for £5,000 in May 1977 and he made a spectacular start, scoring twice in a League Cup tie against Rotherham in September of that year.
Along with Laurie Cunningham and Brendon Batson, who joined Albion in 1978, the trio of black players were nicknamed ‘The Three Degrees’.
He was voted the PFA Young Player of the Year for 1978.