Babayan was born in Gyumri, Armenian Soviet Socialist Republic, Soviet Union, and began his musical studies at age six with Luiza Markaryan, then was taught by pianist Georgy Saradjev, a leading representative of the St Petersburg school and former student of Vladimir Sofronitsky.
[4] His programming covers a wide range of repertoire, often including baroque and classical composers such as Johann Sebastian Bach, Jean-Philippe Rameau, Domenico Scarlatti, Wolfgang Amadeus Mozart and Ludwig van Beethoven, Romantic composers such as Sergei Rachmaninoff, and modern works by composers such as Witold Lutosławski, György Ligeti, Vladimir Ryabov [uk] and Arvo Pärt.
Babayan has collaborated with such conductors as Valery Gergiev, Yuri Temirkanov, Neeme Järvi, David Robertson, Rafael Payare, Gábor Takács-Nagy, Nikolaj Znaider and Tugan Sokhiev.
[8][9] In 2015, Babayan performed two Prokofiev concertos at BBC Proms with Valery Gergiev and London Symphony Orchestra.
[10] In November 2019 Sergei Babayan was Curating Artist at Konzerthaus Dortmund, where he presented a festival of performances with close musical friends, including Martha Argerich, Daniil Trifonov, Mischa Maisky, Sergey Khachatryan, and Valery Gergiev and the Mariinsky Orchestra.