Stepan Kolmogorov was born into a family of company-grade officer. At the age of 15, he joined the Penza Treasury Chamber as a junior clerk and rose through the ranks to deputy head of the department in a span of 11 years.
In 1824, he was transferred to the Yaroslavl Treasury Chamber as an assessor by decree of the Governing Senate, and the following year he was appointed collegiate secretary. In 1828, he was promoted to titular counselor.
During the 1820s and 1830s, Stepan Kolmogorov was sent on missions to various parts of the Yaroslavl Province to inspect the work of local authorities. From 1845 to 1849, he worked as anadvisor at the liquor tax department of the Oryol Treasury Chamber. He retired in the rank of court counselor and returned to Yaroslavl, where he began an independent career as a liquor tax farmer.
In 1835, he was awarded a special badge for 15 years of impeccable service, and four years later the Order of Saint Stanislaus, 3rd degree. He was granted hereditary nobility in 1844. In 1846, he was awarded the Order of Saint Anna, 3rd class, and in 1848, the Order of Saint Anna, 2nd class.
In 1832, he married Varvara Kutkina, a daughter of a court counselor. In 1837, their son Yakov was born, who would become Andrei Kolmogorov's grandfather.
Stepan Kolmogorov and his brothers co-owned estates in the Ryazan Province and a house in Vladimir. During his service in Yaroslavl, he acquired land in the Uglich, Myshkin, Lyubim, and Yaroslavl Uyezds. In March 1838, he purchased a house with annexes, outbuildings, a garden, and a land plot in Yaroslavl, from N. Zykova, a lieutenant's wife. The land plot was located next to the Church of All Saints in Proboynaya Street. Subsequently, the property passed to his son Yakov.
Stepan Kolmogorov died in 1878 and was buried in the Leontievskoye Cemetery in Yaroslavl.