Eugene A. Hamilton was born on February 18, 1828, in Bridport, Vermont, to Amos E. Hamilton. He attended school in Bakersfield, Vermont. He married Martha E. Bump on April 12, 1852, and they had at least five children: Martha, born around 1854; Mary, born around 1858; Eugenie, born around 1863; Frederick, born around 1867; Fanny, born around 1867. They lived in Salisbury, Vermont, and Hamilton worked as a milliner. He also served as a town clerk in the late 1850s. By 1860, he owned $2,000 of real estate and $875 of personal property.
In September 1861, he received a commission as a 2nd lieutenant in Company F of the 5th Vermont Infantry. The regiment took part in the Peninsula campaign, the Battle of Antietam, the Battle of Fredericksburg, the Battle of Chancellorsville, the Battle of Gettysburg, the Overland Campaign, and the siege of Petersburg. He was promoted to 1st lieutenant in June 1862 and then to captain in January 1863. He mustered out on September 15, 1864. He subsequently received a commission as a lieutenant colonel in the 2nd Vermont Militia Infantry.
Hamilton returned to Salisbury after leaving the army, and he earned a living as a merchant. By 1870, he owned $4,000 of personal property. They moved to Brandon, Vermont, in the 1870s. He applied for a federal pension in February 1879 and eventually secured one. He supported the Republican Party, and he presided over a local Republican meeting in September 1880. He died of consumption in Salisbury on September 29, 1887. A local writer described his funeral as “one of the largest funerals ever known in this section of Vermont.”