Danilova attended the Russian Imperial and Soviet State Ballet schools in Leningrad, where she studied under Agrippina Vaganova and became soloist at the Mariinsky (formerly Kirov) Theatre. In 1924 she visited western Europe with a small ballet ensemble headed by George Balanchine. The entire group joined Sergey Diaghilev's Ballets Russes and never returned to Russia. Danilova soon rose to prominence in the Diaghilev company, creating leading roles in Apollon Musagète, La Pastorale, and The Triumph of Neptune. After Diaghilev's death in 1929, she joined the Ballet Russe de Monte Carlo and, as its prima ballerina, made her American debut in 1933 and toured the United States extensively. Danilova appeared as guest artist with several ballet companies, including Sadler's Wells Ballet, and with her own company (Great Moments of Ballet, 1954–56) toured Japan, the Philippines, and South Africa. She won note both for her extensive repertoire, ranging from romantic to abstract Balanchine roles, and for the individuality of her characterizations, particularly the street dancer in Le Beau Danube, the glove seller in Gaîté Parisienne, Odette in Swan Lake, and Swanilda in Coppélia.

Danilova also appeared in musical comedy (Oh Captain!, 1958), taught, and made lecture tours. She played a small but significant role in the motion picture The Turning Point (1977). As a faculty member of the School of American Ballet, she staged excerpts from classical ballets for the annual workshops and staged, with Balanchine, the full Coppélia for the New York City Ballet (1974–75). She also staged ballets for other companies.