He was the son of military commander, general and engineer Abram Petrovich Gannibal, as well as the great-uncle of Russia's most famous poet, Alexander Pushkin.

Gannibal led a detachment of the Imperial Black Sea Fleet, which besieged and captured the Turkish fortress of Navarin during the Russo-Turkish War of 1768–1774, and took part in the founding of the city of Kherson.

At the height of the Russo-Turkish War of 1768-1774, the 34-year-old Gannibal, in the rank of Brigadier, took a leading role in the siege and capture of the Ottoman fortress of Navarino in the Peloponnese.

The Russian Mediterranean Expeditionary Force under the command of Count Alexey Grigoryevich Orlov sent a squadron of ships toward Navarino in April 1770.

During the battle he was aboard the battleship "St. Eustathius" (Russian: Святой Евстафий Плакида, romanized: Svyatoy Yevstafiy Plakida), which exploded and sank as a result of the intense action.

The following year, 1777, he was appointed by Empress Catherine II to a seat in the Russian Admiralty, the supreme governing body of the Imperial Navy.