Born in Bucharest, Cojocaru received her training at Kiev State Ballet School. At 16, she won a medal at the 1997 Moscow International Ballet Competition. Cojocaru joined The Royal Ballet School in 1998 on a Prix de Lausanne scholarship. Six months later, upon completing her training, she returned to Kiev to dance with the Kiev Ballet for a year. Her repertory with the Kiev Ballet included the title role in Cinderella, Swanilda in Coppélia, Kitri in Don Quixote, the peasant pas de deux in Giselle, Princess Aurora and Princess Florine in The Sleeping Beauty and the pas de trios and Hungarian Dance in Swan Lake.
Cojocaru joined The Royal Ballet as an Artist in 1999, was promoted to First Soloist in 2000 and to Principal Dancer in 2001. Her repertory with The Royal Ballet includes Ad Infinitum, Swanilda in Coppélia, Kitri in Don Quixote, Giselle in Giselle, Diamonds in Jewels, Manon in Manon, the female lead in Masquerade, Mary Vetsera in Mayerling, the Sugar Plum Fairy and Clara in The Nutcracker, Olga and Tatiana in Onegin, Juliet in Romeo and Juliet, Odette-Odile in Swan Lake, the Sylph in La Sylphide and There Where She Loves.
Cojocaru’s awards and prizes include Prix de Lausanne (1997) The Nijinsky Award (2004), and the Benois de la Danse (2004). In April 2002 she was given, by the president of Romania Ion Iliescu, the medal of Cavalier of Romania (Ordinul national “Pentru Merit” in gradul de cavaler).
As a guest artist, Cojocaru has appeared with the Kirov Ballet, Paris Opera Ballet, Bolshoi Ballet, Royal Danish Ballet, Vienna State Opera Ballet, Zurich Ballet, La Scala, National Ballet of China, Munich Ballet, National Ballet of Finland, Morphoses: The Wheeldon Company, the 10th and 11th World Ballet Festivals in Tokyo and Corella Ballet and Castilla y León.
She joined the English National Ballet September 2013 as leading Principal Dancer.
Cojocaru appeared as a guest artist with American Ballet Theatre in 2003, dancing Nikiya in La Bayadère, in 2010, dancing Princess Aurora in The Sleeping Beauty and again in 2011, dancing Kitri in Don Quixote. Her repertoire also includes the pas de deux from Manon, Act I and Juliet in Romeo and Juliet.