Fyodor Yakovlevich Bursak was born in 1750 in the noble family of Antonovichs in Kharkiv region. In his youth, he studied at the Kyiv seminary but soon fled to the Zaporizhian Sich, where he earned the nickname Bursak.

He participated in the Russo-Turkish War of 1768-1774 as a private Cossack and took part in Prince Potemkin's campaigns in Crimea. For his bravery and courage, Bursak was promoted to officer rank. He was one of the first to enlist in the forming units of the "Army of Loyal Cossacks" under the command of Zakhar Chepega and distinguished himself in battles during the storming of Ochakov, Hadzhybei, and Izmail. A. V. Suvorov highly appreciated his merits and recommended him for a gold medal.

After the resettlement of the Black Sea Army to Kuban, Bursak was elected as the army treasurer and became part of the army leadership. On December 22, 1799, he became the army ataman and conducted a series of activities to improve Yekaterinodar and the region, established good neighborly relations with the mountain peoples, and opened exchange yards.

In 1803, Bursak founded the first educational institution in Kuban, which a year later became a military school. In 1805, together with Archpriest Kirill Rossinsky, he opened the first library in Kuban. During those years, the Cossacks under his leadership completed the wooden army cathedral and brick wings for housing bachelors. A decision was also made to establish a cloth factory, a horse farm, and a sheepfold.

In 1807, a new war with Turkey began, and Bursak participated in military expeditions beyond Kuban, defending the borders. In early 1816, holding the rank of major general, he retired. He was buried in 1827 near the army cathedral at the Fortress Square of Yekaterinodar.

Fyodor Yakovlevich had two sons, Afanasy Fyodorovich and Pavel Fyodorovich, who also became military men. A. F. Bursak founded a Cossack hundred for the Life Guards Cossack Regiment in 1811 and became its first commander. During the Patriotic War of 1812, the hundred actively participated in the troops of Ataman Platov. In 1812, the Cossack regiment and Bursak's hundred became known as "His Imperial Majesty's Own Convoy." In 1813, the regiment saved three emperors in the battle near Leipzig from an attack by French cavalry and later participated in the capture of Paris. In 1913, the 1st Black Sea Regiment of the Kuban Cossack Army was named after A. F. Bursak.

His grandsons, Pyotr Pavlovich and Pavel Pavlovich Bursak, served in the Black Sea Cossack Army and achieved high ranks.