Yury was the youngest son of the composer's sister Aleksandra (b. Tchaikovskaya, 1842–1891) and her husband Lev Davydov (1837–1896). He graduated from Bonn Agricultural Academy in 1898, and later became a director of the Kiev branch of the Russian Musical Society (1908–1917), and helped to found the Kiev Conservatory.
In 1937 he joined the staff of the composer's house-museum at Klin, where he became curator in 1945. He married Margarita Nikolayevna Lopukhina (1864–1931), and they had four children — Irina (1900–1989); Tatyana (1902–1925); Kseniya (1905–1989); and Georgy.
He died on 16 April 1965 at Klin, and was buried at the town's Demyanovo Cemetery.