Born in a village of Hryazne (today Chernechyna) of Okhtyrka county on November 8, 1888, Kovenko finished his school near Kharkiv in Liubotyn in 1899.

In 1914 he worked as an engineer assistant for servicing mills at the Kharkiv department of merchant guild "Abram Volkenstein and sons".

From October 1915 to July 1916 Kovenko headed a technical bureau of Mechanical Shops department for the Southwestern Front committee of All Russian Land Union (Zemskoi Soyuz).

In 1916 he joined the Ukrainian Social Democratic Labor Party and from July 1917 member of the Central Council of Ukraine where he represents the All-Ukrainian Soviet of Workers Deputies.

In January 1918 as the leader of Free Cossacks he was appointed the city commissar of Kiev of the Central Council of Ukraine.