Born to John Brown Alexander and Barbara King in Elbert County, Georgia, he moved with his family to Williamson County, Tennessee in 1804 and, seven years later, moved to Lincoln, Tennessee. During the War of 1812, he served with the Tennessee Mounted Volunteers under General Andrew Jackson and eventually rose to the rank of first lieutenant remaining with Jackson until the capture of Pensacola on November 6, 1814. As Jackson left to prepare the defense of New Orleans, Alexander stayed behind in Florida. He later served with Jackson during the First Seminole War, however he was discharged after becoming too ill for active duty.