Josiah J. Brown was born on August 29, 1839, in Newark, New Jersey. He grew up and attended school in Newark before enrolling at Rutgers College. He graduated in 1860, and he was studying theological at Rutgers when the Civil War began.
He enlisted in the Union army in 1861, and he mustered in as a private in Company A of the 2nd New Jersey Infantry in October 1861. He later served as a private in Company H of the 15th New Jersey Infantry. He took part in the Second Battle of Bull Run, the Battle of Fredericksburg, the Battle of Gettysburg, the Overland Campaign, and the Shenandoah Valley campaign. He was wounded at Fredericksburg, but he eventually recovered and rejoined the regiment. Confederate forces captured him during the Shenandoah Valley campaign, and he reportedly spent six months in Confederate prisons in Lynchburg and Danville, Virginia.
After the war, Brown attended Union Theological Seminary. He graduated in 1868 and became a Presbyterian minister. He worked in Kansas and Missouri. He married Mary E. Wilcox on June 17, 1868, and they had at least three children: Florence, Elizabeth, and Alice. He later returned to Newark and earned admission to the New Jersey bar in 1888. He died in Newark on January 20, 1936.