Grigorovich was born in Leningrad to a family connected with the Imperial Russian Ballet.

He graduated from the Leningrad Choreographic School in 1946 and danced as a soloist of the Kirov Ballet until 1962.

His staging of Sergei Prokofiev's The Stone Flower (1957) and of The Legend of Love [ru] (1961) brought him acclaim as a choreographer.

Grigorovich has been heading the juries of numerous international competitions in classical ballet.

After the death of his wife, ballerina Natalia Bessmertnova, he was offered the opportunity to return to the Bolshoi again in the capacity of ballet master and choreographer.