William Wirt Daugherty was born on July 14, 1840, in Indiana to Joseph and Mariah Daugherty. His father was a merchant who owned $1,000 of real estate by 1850. He grew up and attended school in Boone County, Indiana, before enrolling at Northwestern Christian University (present-day Butler University). He graduated in 1861 and began working as a clerk.
He enlisted in the Union army on August 19, 1861, and he mustered in as a private in Company G of the 27th Indiana Infantry. According to his service records, he was 5 feet, 9 inches tall. The regiment took part in the Battle of Antietam, the Battle of Chancellorsville, the Battle of Gettysburg, and the Atlanta campaign. He was promoted to sergeant in June 1862, to 2nd lieutenant in October 1862, and to 1st lieutenant in January 1863. He mustered out on November 4, 1864.
He joined the Regular Army in 1867, mustering in as a 2nd lieutenant in the 18th United States Infantry. He was promoted to 1st lieutenant in 1869, and army officials transferred him to the 22nd United States Infantry the following year. He was promoted to captain in the early 1880s. He married Mathilda Anderson around 1890, and they had at least four children: William, born around 1895; Maria, born around 1902; Joseph, born around 1903; and Rebecca, born around 1905. He retired in February 1893 and settled in Indianapolis, Indiana. He died there of chronic myocarditis on February 4, 1922.