Henry H. Covert was born on March 22, 1839, in New Jersey to Minna and Catherine Covert. His father was a shoemaker who owned $1,000 of real estate by 1850. He grew up and attended school in Montgomery, New Jersey. He married Lucinda Van Pelt on December 28, 1861, and they had at least five children: Minna, born around 1863; Mary, born around 1867; Katherine, born around 1875; Llewellyn, born around 1877; and Everard, born around 1882. By the early 1860s, he was working as a shoemaker in Montgomery.
He enlisted in the Union army on February 24, 1864, and he mustered in as a private in Company I of the 1st New Jersey Cavalry. The regiment took part in the Overland Campaign and the Appomattox campaign. He was promoted to sergeant in December 1864. He supported President Abraham Lincoln in the election of 1864. He was wounded in the thigh sometime during the war, and he mustered out on July 24, 1865.
He settled in South Brunswick, New Jersey, after the war and resumed his work as a shoemaker. He applied for a federal pension in September 1866 and eventually received one. By 1870, he owned $2,950 of real estate and $500 of personal property. He returned to Montgomery in the 1870s, and by 1900, he was serving as a justice of the peace. He died on January 20, 1907.