Rozhdestvensky was born in Moscow. His parents were the noted conductor and pedagogue Nikolai Anosov and soprano Natalya Rozhdestvenskaya. His given name was Gennady Nikolayevich Anosov, but he adopted his mother’s maiden name in its masculine form for his professional career so as to avoid the appearance of nepotism.
He studied conducting with his father at the Moscow Conservatory and piano with Lev Oborin. Already known for having conducted Tchaikovsky's The Nutcracker ballet at the Bolshoi Theatre at the age of 20, he quickly established his reputation. He premiered many works of Soviet composers, as well as giving the Russian premiere of Benjamin Britten's A Midsummer Night's Dream and the Western premiere of Dmitri Shostakovich's Fourth Symphony at the Edinburgh Festival. He became general artistic director of the Bolshoi Theatre in 2000, and in 2001 conducted the world premiere of the original version of Sergei Prokofiev's opera The Gambler. Not long afterwards he resigned, citing desertion by singers, production problems and hostile coverage by the Moscow press.
Among the works dedicated to Rozhdestvensky are Sofia Gubaidulina's symphony Stimmen... Verstummen... and several of Alfred Schnittke's works, such as Symphony No. 1, Symphony No. 8, and Symphony No. 9.
Rozhdestvensky is considered a versatile conductor and a highly cultured musician with a supple stick technique. He has been praised for his efficient rehearsals which he keeps short, and is noted for his habit of walking around the stage while conducting and not using a podium, even at concerts.
Conductor Rozhdestvensky is featured in the documentary Notes interdites : scènes de la vie musicale en Russie Soviétique (English title: "The Red Baton"), which examines the hardships faced by musicians in the Soviet Union under Stalinism. In it, he describes the political situation and its impact on his life, as well as those of Shostakovich, Prokofiev, Stravinsky, Richter and other colleagues.
With the USSR Ministry of Culture Symphony Orchestra he recorded all the symphonies of Dmitri Shostakovich, Alexander Glazunov, Anton Bruckner, Alfred Schnittke, and Arthur Honegger. He also performed all the symphonies of Ralph Vaughan Williams in Leningrad in the late 1980s.
He has also conducted many of the world's greatest orchestras, including the Berlin Philharmonic, the Royal Concertgebouw Orchestra, the Boston Symphony Orchestra, the Chicago Symphony Orchestra, the Cleveland Orchestra, the Israel Philharmonic Orchestra, and the London Symphony Orchestra.
In 1969 he married the pianist Viktoria Postnikova.