"He died at 2:30 pm. He had suffered for several years from leukemia and died of respiratory failure," said Rose Torrente-Mett, his sister, also a designer.
Lapidus will be buried on Friday at Pere Lachaise cemetery in Paris.
Edmond Lapidus, known as Ted, was born on June 23, 1929 in Paris. He was the son of a Russian immigrant tailor who opened his fashion house in 1958.
His clients included French film stars Brigitte Bardot and Alain Delon.
President Nicolas Sarkozy paid homage to Lapidus as "the poet of high fashion" and extended his condolences to Olivier Lapidus, the designer's son who continues his father's work, a statement from his office said.