Franklin succumbed to complications from pneumonia on Saturday at a Manhattan hospital, according to his lifelong partner, William Ausman.
Franklin last appeared with the American Ballet Theatre at the Lincoln Center for the Performing Arts three years ago as a friar in "Romeo and Juliet."
"He gave me my first job, and I gave him his last," said the company's artistic director, Kevin McKenzie. "He was a seminal figure in the ballet world."
McKenzie said the amazingly energetic native of Liverpool, England, remembered the greatest 20th century dance moves, starting with Serge Diaghilev and the Ballets Russe de Monte Carlo. He toured the United States with them in the 1950s. "He had a muscle memory," McKenzie said.
"His death puts a period to an era in the dance world," McKenzie said. "He epitomized both the old ballets and the modern ones, and he helped establish the importance of classical ballet in the United States."
Franklin also danced with Britain's Sadler's Wells Theatre and as a backup for Josephine Baker in Paris.