Kedrov was born in Saint Petersburg as the child of a Russian Orthodox archpriest. He was married to Sofia, a singer at the Mariinsky Theatre. From 1894 to 1897 he studied singing at the St. Petersburg Conservatory. As an opera baritone he performed at various theatres such as the Bolshoi and the Mariinsky Theatres.
In 1897 he organized a male vocal quartet which made its debut at the St. Petersburg Conservatory in 1898. The quartet's repertoire included Russian folk songs, ballads, opera music and liturgical music. The quartet successfully toured Europe. From 1917 Kedrov was professor at the St. Petersburg Conservatory.
In 1922, he emigrated from Russia and lived in Berlin. In 1928 he moved to Paris. There he founded another quartet (Quatuor Kedroff) with which he gave guest performances in Europe and North America. Nikolai Kedrov died in Paris on February 2, 1940, at the age of 68. He was buried at the Russian cemetery Sainte-Geneviève-des-Bois in Paris.