He studied at St. Petersburg Academy of arts (1891−97) under A. I. Kuindzhi. From 1900 he worked in Feodosia. The member of associations "World of art","Union of Russian artists", "Fire-color". In the pre-revolutionary period, he wrote mostly species of the Eastern Crimea, stylizing them in the spirit of A. Mantegna and the classical landscape of the 17th century In Soviet times performed a series of industrial landscapes decorative nature.
Born in 1872 in Feodosia in the family of clerk. In 1880 he enrolled in grammar school and in 1881 was raised in a family of Feodosia industrialist Ivan Egorovich Schmitt. He studied first in Feodosia Adolf Faessler, in the Studio of Ivan Aivazovsky, but to no avail. After that, he entered the St. Petersburg Academy of arts he studied from 1891 to 1895 in the workshop of Arkhip Ivanovich Kuindzhi. In 1890 traveled to the sketches on the Volga, in 1897, together with Kuindzhi and his pupils in Germany, France and Austria. There he met with contemporary European art. The biggest impression, according to the testimony, Bogayevsky produced works by artists of the secession in Vienna, and Arnold Bocklin. Since 1900, Bogaevsky exhibited, first in Petersburg, then in Venice, Munich (Secession), Paris and Moscow. In 1904 he joined the New society of artists, then was called up for military service, served in the Kerch fortress, in 1906, was discharged and married Josephine gustavovna the durante. In the same year Bogaevsky was built in Feodosiya workshop, which then worked until the end of life. In 1908 he traveled to Germany in 1909 to Italy and Greece, acquainted with the art of the old masters. In 1910 he was elected member of the Moscow Association of Artists. In the same year he published a book of poems by Maximilian Voloshin "Years of pilgrimage" illustrated with drawings by Bogayevsky. In 1911−1914 years participated in the exhibitions "World of art". In 1912 he completed his most famous work is three panels for the Ryabushinsky mansion in Moscow. In 1914 was again drafted into the army, served about Sevastopol, demobilized in 1918. After the revolution remained in Feodosia, still participated in art exhibitions. In 1923 he worked on a mural for the Agricultural Exhibition in Moscow. In 1933 received the title of honored art worker of the RSFSR. In 1936−1939 year worked in Tarusa. In 1941 was in occupation, died in 1943 in the bombing of Feodosia by Soviet aircraft.
According to contemporaries, Bogaevsky was introverted, conscientious, peaceful and extremely naive person. Closest friends — the artist Konstantin Kandaurov and Maximilian Voloshin.