 Born in a small town near Rostov-on-Don on 17 October 1903, the son of Ukrainian peasants, he joined the Red Army in 1919, where he was a part of the "Budyonny Cavalry".After the Russian Civil War, Grechko was enrolled into the "6th Cavalry College" in the city of Taganrog, which he graduated in 1926.He joined the Communist Party in 1928, and graduated from the Frunze Military Academy in 1936.