When the principal choirboy of the Imperial Court Capella, he drew the attention of the Empress Catherine II, who consigned him to the care of the Italian composer Giuseppe Sarti (1729–1802).
Davydov wrote and published a complete four-part liturgy and 13 Spiritual Choral Concerti, three of which were written for a double chorus.
In the field of secular music Davydov participated in the composing of opera tetralogy Mermaid (together with Ferdinand Kauer and Catterino Cavos, 1803–1807, providing the additional music for the 1st, 3rd and 4th parts).
He also wrote 10 ballets, various divertissements, a series of choruses to the tragedy Amboar and Aurungzeb (1814), a concert overture and numerous other works.
He held the post of the Kapellmeister of the Imperial Theatres in St Petersburg (1806–1810).