Joseph A. Gleason was born around 1841 in Pennsylvania to Joseph and Marilda Gleason. He grew up and attended school in Randolph, Pennsylvania, and his father died in 1857. By 1860, he was living in Chesterfield, Michigan.
He enlisted in the Union army on October 6, 1861, and he mustered in as a sergeant in Company G of the 10th Michigan Infantry. The regiment took part in the siege of Corinth, the Battle of Nashville, the Battle of Stones River, the Battle of Missionary Ridge, and the Atlanta campaign. In October 1863, he assured his mother that “there is not a man in the whole Army who is more capable (physically) of performing soldiers duty than myself. I haven’t seen a sick hour in the past year nor did I see the time in marching 200 miles that I could call myself tired.” He died near Jonesboro, Georgia, on September 1, 1864.