Kagan was born in the Eastern Soviet city of Sakhalin on November 22, 1946. His father was a physician with a passion for music. Young Oleg grew up in Riga (Latvia), studying first with Joachim Braun at the local conservatory, then with Boris Kuznetsov, who would eventually take him to Moscow for study.
Kagan won first prize at the 1965 Sibelius Competition and second prize at the 1969 Tchaikovsky. After Kuznetsov's death Kagan immediately began studies with David Oistrakh and soon found himself in a circle of friends that included Sviatoslav Richter, with whom he would collaborate in numerous concerts. Between 1975 and 1983 they gave a series of acclaimed Mozart sonata recitals, many recorded and later issued. Throughout the 1970s and '80s Kagan's reputation grew as he extended his repertory to include Messiaen (Quartet for the End of Time), Ravel (Duo Sonata for Violin and Cello), contemporary Soviet composer Sofia Gubaidulina (Rejoice!), and works from the Second Viennese School. As Kagan seemed to be approaching the zenith of his career he became seriously ill in 1989. He had several surgeries, but struggled to remain active, touring Europe when he could and arranging festivals. Though his doctors at a hospital in Lübeck, Germany, declared him too sick to be released, Kagan discharged himself to appear at his final festival, in Kreuth am Tegernsee, Bavaria. Shortly after giving two Mozart concerts there, where he had to be helped on-stage, he died on July 15, 1990, not yet 44.