Yakov Kolmogorov was born to a noble family and studied at the Demidov Lyceum. In 1855, he began his career as a scribe at the chancellery of the Yaroslavl Uyezd Nobility Marshal. He resigned from service in 1861. Yakov Kolmogorov was widely involved in public activities and held various positions in nobility and zemstvo organizations. He served as a nobility deputy in the Yaroslavl and Mologa Uyezds and was the Marshall of the Uglich nobility.
Also, he actively engaged in charitable activities. He served as head of the Uglich School Council, acted as a trustee for rural schools, and was a member of various commissions and societies, including the Archival Commission, the Natural History Society, the Society for the Promotion of Public Education, and the Volkov Jubilee Commission. Yakov Kolmogorovchaired the Yaroslavl branch of the Russian Society of Agricultural Poultry Farming. He was also involved in organizing agricultural exhibitions. He was awarded a bronze medal on the Vladimir ribbon "In memory of the war of 1853-1856" and the Order of Saint Vladimir, 4thdegree.
He owned estates in the Uglich and Yaroslavl Uyezds, as well as a mansion in Yaroslavl inherited from his father. He was married to Yulia Trapeznikova. They had five daughters and a son.