Verdy began dancing as a child, most notably with Madame Rousanne and later Victor Gsovsky, both in Paris. She made her debut with Les Ballets de Champs-Elysees in 1945 and danced with Roland Petit's Ballets de Paris in 1950 and in 1953–54. Verdy then performed with the London Festival Ballet (1954–55), La Scala, Milan (1955–56), and the American Ballet Theatre (1957–58) and was principal ballerina in the New York City Ballet (1958–77).

Roles in many ballets were created for Verdy, notably in Roland Petit's Le Loup (1953), George Balanchine's Jewels (1967), and Jerome Robbins' Dances at a Gathering (1969). She also appeared in motion pictures, including Ballerina (1949) and The Glass Slipper (1954). Verdy stopped performing in 1976 to become the director of the Paris Opéra Ballet, and in 1980 she became artistic codirector of the Boston Ballet.