Lacoste, who ran the company for 42 years, died Tuesday in a Paris hospital, said Lacoste's nephew and company spokesman Philippe Lacoste.
The family said Bernard Lacoste had been suffering from a serious illness for more than a year. He stepped down last year as president.
Lacoste succeeded his father, tennis player Rene Lacoste, as president of the Paris-based clothing manufacturer in 1963. The company was founded in 1933.
As heir to the business, Lacoste is credited with making the label more accessible to customers by bringing a wide range of colors to the cotton pique polo shirt, which had been available only in white.
He also started a line of sportswear and accessories for women and in 1981 opened the first Lacoste boutique, in Paris.
Women's Wear Daily reported in 2005 that 42 million Lacoste-branded articles had been sold worldwide the previous year, generating wholesale sales of more than $1.37 billion.
Lacoste polo shirts adorned with the little green crocodile have for generations been the company's trademark. The firm was among the first to put a trademark on the front of its clothing.
The famous insignia comes from tennis legend Rene Lacoste, whose nickname was "le Crocodile." The nickname apparently originated when Lacoste admired a crocodile suitcase in a store window, and his Davis Cup captain promised to buy it for him if he won an important upcoming match.
He never got the bag, but the nickname stuck. Rene Lacoste was the world's top-ranked player in 1926 and 1927 and won seven major singles titles: Wimbledon twice, the U.S. Open twice and the French Open three times.
Bernard Lacoste was born in Paris on June 22, 1931. He received a master's degree at Princeton University and worked for General Motors France as an engineer before joining the family business.
He turned over leadership of the company to his younger brother, Michel, in September but remained "honorary president."
He is survived by his wife, Sachiko, and three children from an earlier marriage.