Joseph Yates was born around 1828 in Charlottesville, Virginia, and worked as a laborer before the war. He enlisted in the Union army on August 20, 1863, in New Orleans, Louisiana, and mustered in as a private in Company D of the 15th Corps d'Afrique on August 27. His enlist records describe him as 5 feet, 8 inches tall.

Yates was stationed in New Orleans and Brashear City, Louisiana until February 1864. On February 10, the army re-designated his regiment the 5th Corps d'Afrique Engineers. From March 10 until May 22, the men took part in the Red River Campaign, a failed Union attempt to establish a base in western Louisiana for use in future expeditions in Texas. They primarily served as construction workers during the campaign, building bridges, fortifications, roads, and dams in the areas around Grand Ecore and Alexandria, Louisiana. On April 4, the 5th Corps d'Afrique Engineers became the 99th USCT Infantry Regiment. The men performed fatigue duty until June 20, when the army ordered them to New Orleans. They remained there until December. Yates transferred from Company D to Company G on November 23, 1865, and the army placed him on detached service at the arsenal in Apalachicola two days later. He mustered out on April 23, 1866, and then disappeared from the documentary record.