Svetlana was born in Yadrun, Russia, just outside of Moscow. In 1997, she completed formal training at the Ufimsky Choreography School, which is now named the Rudolph Nureyev Russian State Ballet Academy.

Upon graduation, Todinova joined the Krasnodarsky Musical Theater troupe of the Bashkiria Theater, where she danced under the direction of Yuri Grigorovich. In 1999, she became a member of the National Academy of Theatrical Arts, also known as "GITIS," with which she toured internationally.

In 2006, Todinova was invited to join the Crown of Russia Ballet Company as a soloist, continuing her international tours. Her repertoire includes Don Quixote, Sleeping Beauty, La Bayadere, Carmen, Swan Lake, The Nutcracker, and more. She danced with the Moscow Ballet since 2001, also serving as Moscow Ballet's Audition Director. In 2011, Svetlana led Moscow Ballet’s Summer Intensives. Following this, she joined her colleagues for the 60-city North American tour of Romeo and Juliet and the Great Russian Nutcracker.